Understanding Light's Dual Nature in Physics

Hello, Hello, Hello my warriors and today's session is going to be a very interesting one for all the NEET students who want to crack the NEET exam this year or even next year. A very important chapter of dual nature just like the movie of Parijit and if you have seen this movie you know how the hero has two split personalities and then the same thing happens with light too. Light sometimes is like hey I have momentum I'm a particle and then light is next moment like okay I can bend I can spread so I'm a wave and then light is like hey guess what I have you know energy and I have you know radiation pressure I can hit something I can apply pressure and the next moment light is like okay I can also interfere with each other and I can also create constructive destructive interference so light has this very amazing dual split personality and that's this hero who was trying to tell you at that point of time that Shreyas sir is going to teach you this chapter in one shot so that's the promotion of this series zero to super hero he's a hero of course actually a superhero and he's telling you you guys are going to get this in one shot all right so i hope let's we are going to complete this in today's class uh hello nani vandana party hello hello neat spot welcome anthony welcome dalijan yes it's onion i know i know and how many of you have seen onion yeah Raise your hands. Is this coming in term 2? Yes, it is coming in term 2. Definitely. Neelarjanan, hello, good evening. So, those of you who do not know me, my name is Onion, oh sorry, not that Onion, my name is Shreyas and I am the physics master teacher and I have been doing lots of things, you can read it out here, blah, blah, blah, blah, blah and you can also follow me on Instagram. Okay, cool. So, let's get started and yes, we are going to see. A lot of things today, dual nature, photons, properties, photoelectric effect, Thoms and Slutdorff model, Bohr's model, hydrogen spectrum, all of this in today's one shot just like Anian said. Yes, Sundar, oh my god, my secret is out. Okay, it's not a secret actually. Anian, actually the spelling of onion is not O-N that Kanda, no, no, it's something else. A I think, A-N-I-Y-A-N, okay. Cool! Dual, dual means Ankit this is dual. See this, this is dual. This, you are this and then that, that's dual. This is one, okay so that's one and what you see behind that one that's dual. You have some personality this side, some personality the other side. So that's dual. You have a dual personality disorder. So that's what it is. Alright, cool. So, In the first part of this session let's talk about the dual nature of light like I just told you. Light sometimes shows particle like behavior as in it shows properties like momentum, force just like when you throw a ball on somebody's face. Have you thrown a ball on somebody? Please don't do that. Okay so obviously you will get hurt. It has some momentum it will exert some force and if you throw balls you know through an opening the ball will pass through the opening without getting deflected. straight ahead of that opening. It won't bend just like Rajnikanth does when he shoots bullets from his gun. The bullets bend, that's weird because the bullets are particles but that's Rajnikanth again. So that's an exception. And it also shows properties like interference. It also shows properties like diffraction, refraction. All these are the properties of waves. So we have associated dual nature for light. It's like okay you exist together, no problem. we have no issues whatsoever yep is this complete section yes ribaka definitely good evening chandra leka wow i like your names guys amazing names nilarjan such powerful names anurag joseph samrat look at the name mansa ready my god chandra leka vandana alw crazy anthony gerard vignesh rasuri amazing names you guys have proud of you okay so according to einstein The particle nature of light what is it called? Photon. Photo? Photon. Okay. So a photon is like a packet of energy which carries energy and these packets travel very fast at the speed of light and these packets when they hit something when they interact with other matter they transfer their momentum to that particle they create an impact they create an impulse ok and each packet like I told you it has photon which is called as a photon has some energy I'll give you that energy formula and all the important details about the photon these are the most important properties which you should know you know from the theory point of view for board exams also from neat point of view. So photon always travels at 3 lakh kilometers per second or 3 into 10 to the power 8 meters per second in vacuum and it doesn't matter how you see the photon. So that's very weird but you know it's true that no matter how fast you travel you will always find the photon traveling at 3 lakh kilometers per second. Okay now the energy of the photon is given by this formula. I'll just put it up right over here. The energy is given by the energy of your photon is given by h into f. But we all know the speed of light is frequency into the wavelength. So frequency can be replaced by c by lambda. So you can also write it as h c divided by lambda. This works. All right. Very good. The week we will start in a minute. Just hold on for some time. Yes. And the photon is the energy particle so it has no meaning at rest. The rest mass is zero. So when you see a photon at rest that means something impossible has happened. You can never see the photon at rest because the photon always travels at 3 lakh kilometers per second. Even if you travel very fast photon will appear to travel even faster. So you know it's always constant so you can never see the rest mass but it has been assumed to be zero. So, lot of people think, sir, the mass is zero, sir. Then, the momentum will also be zero. That's the funny part about photon. This is a very fascinating chapter. You think this, this should not happen, but that will happen. You think that should not happen, that will happen. So, mass is zero, but it still has momentum. Photons are neutral and stable. They won't decompose. They won't combine together to form new things like atoms do, like they split or they combine to form molecules. and they get and they do not get deflected by electric or magnetic fields, which is obvious because it does not have a charge. Now, the rest mark is zero, but it has momentum, but it has momentum. And what is the momentum of a photon, the momentum is H by lambda, that's very, very important, you should know this. And if you take this, P and substitute it over here. You can see H by lambda is right over here, right? H by lambda is right over here. You can definitely write it in terms of momentum as well. Yeah, momentum is E by C, you can substitute all these things up to you. Yes, expectation and reality not equal to. Can I start class 12 with modern physics? Not a good or a great idea, Ayesha. You should start it probably with other chapters. Okay. But yes, if you are in NEET 2022 or JEE 2022, yes, you can start. But if you are 11th to 12th moving, then don't start. Okay, great. Now, there is another concept which is called as the radiation pressure or the radiation force. So when light falls on your face or when light hits something, it applies a force. That force is small, but it is still there. And we can find that force out depending on whether the object or the surface on which it is falling is an absorber or whether it is a reflector. So if light falls on a surface which is absorbing in nature it falls and it gets absorbed then the change in the momentum then the change in the momentum is final momentum minus initial momentum that's it and you can calculate and you can calculate This momentum, okay, magnitude wise, you all know, it is nothing but, you know, h divided by lambda, that's it. It's nothing but h divided by lambda, that's the wavelength of this light. But if, if the surface is reflective in nature, it will change its momentum in the opposite direction. In that case, the final momentum change or the momentum change will be final momentum minus initial momentum. So magnitude wise you are going to see that the final momentum is exactly negative of initial momentum. So that's the reason why you will have minus pi minus pi but you're taking the mod so it will be basically two times the initial momentum or two times of h by lambda. Is that right? Everybody got it? Yes. Excellent. Very very important. Now also I'll give you one more important formula which you should know. If light is falling on a surface and it has an intensity p. It has an intensity of I. What is the meaning of intensity? Intensity means how many watts of energy is falling per unit area. How much is the energy which is falling per unit time per unit area. That is intensity. If the intensity is given then on any surface which has some area A, the pressure. The pressure which is also called as the radiation pressure is given by I by C. I by C, intensity by speed of light and the force because force is pressure into area. It will be nothing but I by C, the whole into A. So the force on that surface will be I A by C and the pressure obviously will be I by C. This is if it is absorbing. This is if it is absorbing. Okay, if it is absorbing, if it is reflecting, what will you do guys? What will you do? What will you do? Come on quickly tell me you should be able to tell me this. What will you do if it is reflecting in nature? What will you do if it is reflecting in nature? This is absorbing. So that's why it is IAYC. But what will you do if it is reflecting in nature? If it is reflecting in nature, you are just going to multiply it by two. That's all. That's the change. Yeah. 2i by c perfecto great now let's move ahead and here comes another interesting hypothesis given by de broglie so light shows wave and particle wave is when it goes and interferes young's double slit experiment particle that's the photon nature which it has momentum force pressure all of those things even matter like us electrons protons you They also have dual nature. Usually your particles around you show particle behavior. Your bottle shows particle behavior. But in a very microscopic level, at a very quantum level, when you zoom in, things look very different and it can show wave-like properties. So for a particle of mass m moving, Moving with momentum moving with momentum. Okay, P the matter wave the matter wave the matter wave is the wave associated with a particle not with a photon. It is not an electromagnetic wave. It is not a sound wave. It is not a wave on a string. It's not an earthquake. It's a different kind of wave which is not possible for you to visualize or see through your naked eye. The matter waves, the matter waves wavelength, wavelength which is also called as the de Broglie wavelength is given by h by p. If you notice this formula is very much similar to the previous formula. I'll show you over here. P is h by lambda. Just shift lambda there, put p down. You will get the de Broglie wavelength for a matter wave. That's it. As simple as that. Yes, you would have learned this in chemistry. Very good. Excellent. Yep. Now, once you know this, you can also substitute momentum as terms of energy like this. The kinetic energy of a particle, the kinetic energy of a particle k will be half m velocity square, which is also the momentum square by 2m. You can substitute momentum as mv, you will get the same expression as before. Hence from this momentum will become 2mk but that's the square of the momentum so momentum will be the root of this. You can even substitute it over there and this will be nothing but h by root of 2mk. This is only for particles of matter mass something which has mass like electron proton bottle pen my hand you watch air everything so that's when you will use this formula but when you are talking about light or electromagnetic waves then this is the energy formula you will use or this is the momentum formula that you will use. Are you getting the difference? Light is an electromagnetic wave. Electric field, magnetic field, completely different. The particle nature of light is called as photon whereas the general particles around you electrons, protons, neutrons they have a mass m, kinetic energy k. And their matter wave which is completely a new kind of a wave like sound wave, wave on a string that is having a wavelength of h by p. P is the momentum of that particle. Completely different. Okay time to join the week quiz using the code 224283. It should be also pinned in your chat box. I have also shared it on the telegram channel and another way. is going to the description box and then joining it using the link and another way is just going to vedantu.com slash v quiz and entering this code that's it either ways you will be able to do it yes free car i will do it okay so come on guys start joining the class right away and i'll be starting the v quiz in no time okay so go to www.vquiz.in and use the code 224 283 or you can directly click the link which is there in the chat box and then you can start. Alright come on guys waiting for all of you to join go ahead and start joining the V quiz right away because it's going to be fun and throughout the session we are going to have V quiz after every theory concept that I'm going to teach hopefully the V quiz works today. No Ankit there is more theory because there are more topics as well come on I'm going to start the first question Usually you will get 45 seconds. Some questions towards the end will have around 60 seconds. Alright, are you guys battle ready? Okay, are you guys battle ready? Okay, come on, come on, come on, come on my warriors. Join in. This is Kavya for 12th standard students. But if you are 11th standard student, you can still join in. Because you would have definitely studied this in chemistry. Definitely. Hello, Hare Krishna. Welcome. Hi, Janhvi. Hello, Rama. Hello, Reshma. Hello. Welcome, welcome, come on join in, join in Ankit, join in Srikar, come on. Alright, one minute, I'm going to start, within one minute I'm going to start. Alright, so get up, we have decent number of people and I'm going to start any moment. Oh by the way, let me also tell you, even if you are watching this session recorded, you can still join the VQuiz, although you might not come in the leaderboard, but you will still get points and you can compare yourself with the students who participated live. That's a very cool feature of V quiz and that's how you can even participate in all the class quizzes even after the live class is over. But yes, the fun of a live class is completely different. All your attention on the screen. I'm starting the quiz in 3, 2, 1, go. Here is the first question on your screen now. Yep, I've started. Can be, Harchini this is a Neat Channel plus J channel. Yes, you can definitely use Harshini for NEET. Exactly, this is for NEET. Please read the description box guys. When a high-energy UV photon beam enters the electric field, it will be? Come on, this is an easy peasy lemon squeezy question. Accelerated, retarded, undeflected, none of these. Okay, make sure you write or post answers only in the week with nowhere else. So come on, an introductory warm-up question for all of you just to brush up your concepts. Today's lecture is all about concept revision and formula applications. Okay, Ara not here, you have to go to vquiz.in, Ara Vindhan, go to vquiz.in and enter the code and participate there. Malik, Moni, go to vquiz, not here. Okay, time is running out in hardly 10 seconds. Divya, not here, not here, go to vquiz, go to vquiz, participate there, that's the fun. There is no fun here. Alright, so let's have a look. I would request the admin to block the students who are going to put the answers over here. Okay, so accelerated wow and undeflected thank God. Yep, that's the answer guys. How will it be? Okay, let's see the result. Okay, so look at this guys. So many of you answered it wrong. Why will it be accelerated? A photon is a charge less particle and when you pass it through electric or magnetic field it has no effect on it. because there is no charge there is no north pole or south pole so hence there will be no change in its velocity Good evening Alpha. Okay, so let's have a look at the leaderboard. Who is this? Anuraj, Rosh and Dalijan. Very good, Janhvi. Very good, Joel, Dhruv, Srilata, Priyanka, Yuva Deep and Parithi. Excellent. Moving on to the next question. Get ready on your screen now. Question number two. Let's see how many of you can answer this. A radiation of energy E falls normally on a perfectly absorbing surface. The momentum transferred to the surface is which of the following options? Okay, come on my warriors figure this out if energy Falling if the radiation of energy e is falling on a perfectly absorbing surface Then the momentum transferred is e by c to e by c e c e by 2 c Interesting. Yes alpha you can definitely join in there is nothing that you have lost. Okay, join in go ahead and participate You will have fun. Even if you are watching the video right now, is it e by c? Is it 2 e by c? Is it e c or e by 2 c? okay let's see how many of you can answer this question 24 seconds this is straightforward direct come on I want you to fight it out but the catch is who will answer it very quickly all right and the time is going to be up in five four three two one and showdown I guess Yes, some more theory, yes Ankit, lot of theory to come. Yes, definitely, definitely. Let's have a look at the results and this is how our students have answered. Some of you have answered E by 2C, E by, E C also, 2E by C also and E by C. Oh, okay. Perfectly absorbing surface, the momentum transferred, actually it should be A not B. This is wrong, this should be correct. Oops, sorry guys. I think somebody who made the quiz. gave a wrong answer over here it should have been E by C if it was to E by C it should be reflecting surface so I'm not going to show the leaderboard let's just skip to the next question it should be E by C E by C okay I mean if you look at it this way also look at it this way that the perfectly absorbing surface then the momentum transferred so if it is getting absorbed then the change is only E by P But if it is getting reflected, if it is getting reflected, then the change in momentum will be 2p. So the two factor comes only in case of reflecting. Yes. Okay. So let's just move ahead to the next question coming up on your screen. I'm not going to show the leaderboard. Question three on your screen now. Okay. So Sri Harshit, you got Ekalavya. Proud of you. Make the best use of it. And you're going to rock it. Hope to see you soon. during the victory celebration when you crack J advanced. Okay, if the kinetic energy of an electron is made four times then the de Broglie wavelength will then the de Broglie wavelength will come on come on come on come on. Okay, come on. Let's see how many of you can get this. Okay, come on, come on, come on, guys. Let's see how many of you can get this. What is this? Oh my god! Eeeh! Hari! What do you mean by that man? If the kinetic energy of an electron is made 4 times, then what do you think is the de Broglie wavelength? What do you think is the de Broglie wavelength going to be? Come on! Come on! No, no, no! Don't answer over here. Don't answer over here. Try to answer in the V-Quiz itself. I wanted you to participate in the V-Quiz to get a feel of your mock test or your actual examinations. Alright! Let's have a look! How many of you got the correct answer? Wow, very good, very good, very good, very good. See guys, what happens is if the kinetic energy of an electron is made four times, then what will happen to the wavelength? De Broglie wavelength is your energy, okay? I'll just put it like this. De Broglie wavelength, De Broglie wavelength is h by p and your momentum is root of 2mk. isn't it? Root of 2mk. I just gave you that formula. If you notice over here, this kinetic energy will become 4 times but it is under the root. So, root of 4 is 2 and it is in the denominator. So, hence this wavelength will become 1 by 2 times and 1 by 2 times means it will decrease by 2 times. That's it. That's all you have to think about. Okay, just use the formula. That's it. Alright, let's have a look at the leaderboard now and see what the scores are looking like and then we will go to the theory part. Wow, we have Abu Raj still at the top, 2939 points. Joel, Janhvi, Anthony, Srilata, Ankit, Harish, Abhinash, Rosh and Kavya. Very good, Bacha Log. I will not show you the next question because the next question will come after some time because we have to go with the theory part now. Alright, so let's go to the theory of the next topic and that is the photoelectric effect. See, we just talked about how light can behave both like a wave as well as particle and normal matter can also show wave-like characteristics whose formula is given by de Broglie. Now based on the concept of photons, The photoelectric effect can be explained. Photoelectric effect is nothing but when light of sufficiently high energy falls on a surface then electrons are ejected out and if the electrons are collected and you connect it across a circuit you will see a current which is established in the circuit. This phenomena where electrons get ejected out because of high energy light that is called as photoelectric effect okay the electrons which are ejected out they are called as photo electrons photo means light so electrons ejected because of light are called as photo electrons number two number three because the electrons go to the other side and they will start moving around in the circuit so there is a current that current is because of light again hence what will it be called Photo current as simple as that. I hope this is clear. Yes, I do remember Rohit Kolthai. Yes, definitely. Now, now ejected means it is thrown out. It has been ejected like you would have seen some movies or maybe some documentary where there is a pilot and because of some malfunction in the plane, the pilot ejects out of the plane. He's thrown out of the plane, okay, by himself. So, that is what is ejection basically. Okay, now what happens is we need to understand the different parameters related to frequency, intensity, is there a relationship with the current and can I somehow increase the current by connecting a battery or reversing the polarities. Also what will be happening if I change the plate over here, will there be any effect on the current or other things. This plate is usually metallic in nature because what is the speciality of metals. They have free easily ejectable electrons. Things like plastic or wood, they have electrons but it is very difficult to knock the electrons out. So usually you will use a metallic surface where you have easily removable electrons so that a photo current can be established. Great. Next, so let's talk about all the important aspects about you know photoelectric effect one by one. So You should remember this setup always. You will always see the light will be falling on one side, photoelectrons will be ejected from that side and they will be collected and they will be establishing a current in the circuit because if the electrons go like this then actually the current will be going the other way around. Just keep this diagram in mind. We are going to solve a lot of problems. Now why should the light be of a sufficient wavelength? or a certain energy. Okay. See whenever there is a free electron inside the metallic surface it's not truly free. It's not exactly you know free in the sense you do not need any energy to take it away. You need to pay some tax. You need to pay some commission to take out that electron because that electron is still slightly bound to the atom inside that metallic surface. So, if you notice these are different colors of light and you would notice this is red, this is green, this is violet and in red color light when it is falling on the surface there is no electron which is coming out but in green yes you have in violet or blue you have some electrons coming out. What is the reason for this? Red has a very less frequency or large wavelength. Hence the energy is less. The energy of photon is less. But in the case of green photon, the energy is more. In case of violet, the energy is even higher. So therefore, you would now realize that there is a critical frequency for which the photoelectric effect will occur. After that, below that frequency, you will not see the photoelectric effect occur because the photons do not possess that energy to knock that electron out. Okay, it does not have sufficient energy to knock that electron out. Okay, so that energy, okay, that energy which is required or that frequency which is required to knock that electron out is called as the threshold frequency. What is it called? It is called as the threshold frequency because that is the frequency only after that you will see photoelectric effect which will occur. That is generally denoted by the symbol f naught. and photoelectric effect, photoelectric effect occurs if f more than f0. If f is less than f0, it will definitely not occur. Now, what is the relationship of this frequency with some other parameters of the entire photoelectric setup? How do you think this F0 is decided? What is that thing which affects F0? Who decides the value of F0? Can you guess? Can you guess? Think about it. Critical means that's the minimum frequency after which the effect will occur. Remember the energy of a photon energy of a photon is HF blue light Violet light has very small wavelength, high frequency. So more energy. Red light, large wavelength like you can see. So less energy because less frequency. So that's the reason why I said more the energy of the photon, the good that better the chances is for the effect to occur. And the minimum critical, that's the limiting. He's in the critical stage, meaning you do not know what is happening. Okay, what can happen? So after that only, You can decide okay if effect is going to occur or if the photoelectric effect is not going to occur. Yes, I hope Girishma, Janhvi, all of you have understood it. Kavya, everyone. Hello Mahesh. Welcome. Yep. Is this clear? Yes, I'm going to come to photoelectric equation also. Now that critical frequency, the frequency required to throw out that electron depends or that critical frequency required to start that effect depends completely on this metal. See, imagine you are holding something which you like. What do you like guys? Maybe you like ice cream, maybe you like chocolate. You are the atom. You like your toy, maybe a teddy bear or maybe a chocolate. You're holding onto it. Okay, I'm just going to imagine I love this bottle. or I love what is in it, maybe it has some very nice mango juice or lime juice, I don't know, whatever, I'm going to hold on to it. Somebody comes with very high energy and he knocks me out and he takes it away, he takes it away. If that somebody coming from that side has very little energy then I will not give it to him. If he comes from that side and he tries to take it, I will hold on to it. If somebody with very high energy comes, There's a very good chance he can knock it out and take it from me, snatch it from me. Now imagine I am little bit stronger or I am little bit weaker. If I'm weak, I hardly have a grip on this like this, then the person comes from that side, he will snatch it away very easily. So the minimum energy required for snatching that or ejecting that electron depends on the metallic surface. Understood guys? Somebody saying laptop. Hi Agadish. Very good. Very good. Excellent. Nature of the metal. So this F0 depends completely on the metal surface and that minimum energy required, that minimum or critical or critical energy required. What is that minimum or critical energy required called? That is called as your work function. What is it called? It is called as your work function and that will be equal to HF0 which is the energy of the photon obviously. That energy of the photon which is needed to just throw out that electron is called as the work function. Very good. All right moving on. This work function like I told you it depends from a metal to a metal. to the next metal like gold might have different work function, aluminum might have different work function. As a minimum quantity of energy required to remove an electron. Okay to completely eject out that electron. Okay. I hope all these definitions are very very clear. Excellent. Now, let's talk about the next part and that will come over here. Here right now there was no battery but imagine there is a battery. Okay, let's try to understand. See these electrons which are ejected the electrons go like this and follow this path that means the current which is established in the circuit will be exactly in the opposite direction. This is how. The current is established. This is how the current will flow in the circuit. If somehow you place a battery, you place a battery and you push the current or you help the current, more current will flow. Like for example, if you place positive terminal here, negative terminal here, what will the positive terminal do guys? What will the positive terminal do? It will pull more electrons. It will happily pull more electrons. that will increase the current. More current will flow obviously but if you connect the battery to oppose the current, if you connect the battery in the opposite manner then the current will decrease and that's what I want you to see in the next GIF and animation. Observe this, observe this. Look at this, in this situation the light is falling, light is falling, electrons are ejected and slowly you are changing the current. slowly you are changing the current and how are you changing the current by increasing the voltage look at this 1 volt 2 volt 3 volt so when you increase the voltage what happens is that the positive terminal is connected here positive will pull more and more electrons so the current will increase naturally it will increase yes work function is energy go cool threshold frequency is hertz frequency. Phi is HF0 and they both are related more frequency threshold frequency more work function but one is energy one is frequency units are different there are two different physical quantities go cool. I hope this is clear. Next important thing that you should realize that if you reverse it like over here you can see that when you increase the reverse voltage the electrons which are ejected out feel resistance to reach here because now the negative terminal is connected here. Negative, negative repels. So you will see the electrons which are reaching now face a lot of difficulty and there could be a potential, there could be a potential for which, for which the electrons are no longer able to reach here. The potential or there is a voltage for which when you increase the voltage after that, there is no further reaching of electrons to the other side. That reverse voltage for which you stop the flow of electrons is called as the stopping potential. Electrons are ejected out. Okay, electrons are ejected out and you are like stop it or stopping it by creating reverse voltage. So that minimum voltage for which the electrons stop is called as the stopping voltage or stopping potential. I hope this is clear. And that minimum energy. that energy minimum to stop to stop the photo photo electrons. We all know we all know that the voltage difference applied to a charge causes acceleration or deceleration. Here it is causing deceleration. So voltage difference of V volts to a charge of the electron which is E causes an energy difference of how much charge into voltage. Remember this formula. This is standard. This is in electrostatics. The energy due to the energy due to acceleration or deceleration is nothing but the charge into potential difference. Do you know this formula? In case you have forgotten now remember it. Energy difference is charge into voltage. So that minimum energy which is required to stop it, so you have changed the energy of that electron so that energy required to decelerate it will be the charge of the electron into the potential difference which is Vs. This Vs is your stopping potential, stopping potential or stopping voltage difference. Is that clear? Yeah, it's something like a capacitor but in capacitor the electrons don't move between the plates, they move from the outside part. Here the electrons are moving between the plates in that area. Empty space. EMI for this part? No. Yep. Yes, it could be. It could be mixed with magnetism as well. Yep. All right. So, be stable. I'm teaching in the 12th standard batch, 11th to 12th moving batch, also in the crash course, which is for the 2022 students. Okay, fair enough. Now, let's come to the main part, which is the Einstein's equation. Einstein's equation. A lot of people get confused, I don't remember, sir. How to remember? Please help me. I will help you out. You make it like a story. I just told you what do you love guys? It could be laptop, it could be Dairy Mill silk, it could be bottle, it could be teddy bear, it could be anything. Okay, you're holding on to it. Some person comes with a lot of energy snatches it away. When you are resisting, you are sucking away some energy from him because he's going to knock you out and you're going to resist. He might come with a lot of energy but while resisting he will lose some energy because you are going to make an effort to not lose it. But anyways he snatches it and the precious thing goes away. So he will have little he just took away this bottle now this bottle will fly off okay but it will have some less energy. Same thing happens here look at this now look at this light is falling on an atom of the metallic surface it knocks out that electron and the rest of the energy is used as kinetic energy. So what happens is that the energy of the photon goes in knocking it out, knocking it out, knocking or basically ejecting it out and the rest of the energy is the kinetic energy of the electron which has been ejected. So, what is the energy of the photon guys? It is HF, isn't it? It is HF. What is the energy required to knock it out or eject it? It is the work function. And what is the kinetic energy of the electron? Well, I'll just put it as Ke. That's it. So this is your basic, you know, or the most elementary level of writing the Einstein's photoelectric equation. The photon's energy goes in rejecting it and the remaining goes as kinetic energy. Now I just told you the formula for phi. Don't forget it. What was the formula for phi? It was nothing but HF0, isn't it? Work function, the minimum energy required. happens at the threshold frequency minimum frequency that is hf0 okay is the energy now kinetic energy how do you measure the kinetic energy of the electrons the kinetic energy is measured by this formula evs tvs is the energy required to stop it that's the least energy you require to stop it after that you will never see the photoelectric effect because it will not come to the other side you will not see current sorry you will not see current into that circuit so you're absorbing all the kinetic energy of the electrons it came with full josh it came with full josh and then you stopped it and it went back so you're absorbing that kinetic energy hence the kinetic this measures this whole thing measures okay the kinetic energy of the electron and hence i can just write this as E into Vs this becomes your more advanced version of writing the same equation. I hope this is clear. No crash course lectures you know are still available for you to view it as a recording in case you had joined before but if you are planning to join now then you can still join and watch all the lectures you can also give the test at your free time. Okay so both the equations are very easy. Very important. Is that clear? Can we move ahead to some more questions? Also notice one more thing intensity has no role to play in all of this except for the fact that if the light is more intense if the light is more intense if I can put if light if the light is intense then I can put a light on the other side of the screen. There are, there are more photons. Then there are more photons. If there are more photons, what does it mean? More photons will eject more electrons. So there will be more, there will be more photoelectrons, more photoelectrons. If there are more photoelectrons, what will happen? The current in the circuit will also increase. Keep this in mind. very good okay great no Jayant I do not teach good in crash course I teach very bad I teach only good in some places why will I teach good in crash course what is there no obviously I don't teach okay so let's go ahead to the next quiz coming up on your screen so what is K max equal to Aishwarya K max is exactly this the max kinetic energy of the electron you have absorbed it why max kinetic energy why all electrons have different kinetic energy because they will have trouble getting out some electrons will have lot of trouble to get out of this plate some electrons will have less trouble. The electrons which have less trouble getting out they will have more kinetic energy so stopping them will be more difficult. Understood? If electron has less difficulty to come out it will come with a lot of energy so we'll have more difficulty to stop it. So hence the maximum kinetic energy is measured by you know measuring the stopping voltage. So the last most luckiest most energetic electron if you are able to stop it, then for sure you have stopped every other electron. Okay. And yes, some students were like, Sir, what's the what about the graphs? Well, I can show you certain graphs like this, this one very, very important graph, like this one over here, the current versus the voltage. And if you look at the current versus the voltage graph, the graph will look something like this. This is your negative stopping voltage. This is zero volts. This is your positive voltages. The current increases and it saturates. It saturates at a point. It saturates. Why? Because after a point all the electrons are ejected. How many more will you eject? There are only a limited number of electrons. So you can only emit or you know, emit electrons as many as you know photons are falling onto it. If 10 photons are falling, 10 electrons will eject. So beyond that you cannot increase it. And if you increase the intensity, and if you increase the intensity, then what happens? If you increase the intensity, then you will see the graph go up. This is for more intensity, which I just told you. When intensity increases, then the current also proportionately increases. This is for more intense light. This is for more intense light, which is very, very important. You should know this. Jayant, we teach the same way or you can say, you know the teaching style could be different but we put in our 100%, 200% efforts both on YouTube. YouTube teaching is different because this is on this big screen and you know the kind of interaction we have is different. In crash courses or on the Vedantu platform, we have another teacher to help you out. There are lots of quizzes and there are leaderboards and so many other things that happen. apart from assignments and all the tests that happen so you know that there is a systematic way of way you know things happen okay so the teaching will be or style will be different but the content or you know uh the the teacher energy will be the same don't worry about it all right so here comes the next quiz on your screen get ready to join now and let's see if you guys are there okay let me just put it right up on your screen. Okay, I'm starting the next question on your screen. Okay, I'm starting the question on your screen. Get ready. Make sure all your attention is towards V quiz. Okay, here it comes on your screen now. Alright, so what do we have over here? When photoelectric effect if the intensity of light is doubled, then the maximum kinetic energy of the photoelectrons will become? Come on, think about it. Think about it. If the in the photoelectric effect if the intensity of the light is doubled then the maximum kinetic energy of the photoelectrons will become how much? Hello Maha Lakshmi. Welcome. Welcome. Participate in the quiz. Come on. Double half four times no change. What is the answer? In the photoelectric effect if the intensity is doubled then the maximum kinetic energy of the electrons will become. Hi Isha. Welcome. Okay. Will there be 11th class from the start for 10th graders after the boards in this channel? Please let me know. We will have the 11th standard classes, Tarun, but in a very different manner. Okay, let's see the final answer in 10 seconds. Okay, come on, come on, come on. 9, 8, 7, 6, 5, 4, 3, 2, and there we go. We have it on your screen. A lot of you are saying no change, is it? Yes guys there is no change. Reason if the intensity is doubled kinetic energy has no effect on it because when you change the intensity Then the number of photons will increase but the energy of a photon will never change. Each photon still has same energy just the number of photons will increase which will increase the current but the energy of a photon is still going to be the same. Hence the kinetic energy will also be same. Just that there are more in number does not mean they will have more kinetic energy. It's just that more electrons will be ejected. That's all. Let's have a look at the leaderboard coming up on your screen now before we go to the next question. Wow, Joel has gone to the top. Proud of you. Then Anbu, Raj, Anthony, Daljan, Janvi, Lok, Vishnu, Manogiana, Priyanka, Shrilata and Yoadeep. Very good. Keep fighting guys. Things can keep changing. Moving on to the next question on your screen now. Get ready. All right. So what do we have next? A photosensitive material would emit electrons if excited by photons beyond a threshold. To overcome the threshold, one would decrease the... Interesting question. Come on, figure this out. To decrease, to overcome the threshold, one would decrease the... What? Think carefully. What would you decrease? Come on my warriors. Voltage applied, intensity of light. wavelength of light or frequency. Quiz is not working Janhvi or you actually it should bacha. Just go to vquiz.in and just enter that code or just click on that link or was there a time limit for entering it? I don't think so there is a time limit you can join in at any point. Let me try it out on my phone bacha. Okay let me just try it out. Okay, one second. I'm just trying to log in through my phone and see if it works. You need to log in, I think, through your Vedanto ID. Even if you are not a member, you can still become a member by creating a free account. Even if you have a free account, it works, guys. I'm just trying to join in. Meanwhile, I'll show you the results. Oh my god, one second, I'm entering the wrong password or email ID. I'll check it out later on. Show the leaderboard. Okay, let's have a look. Guys, guys, guys, guys, guys, for the previous question, what was the previous question? It was all about you know, the threshold. What if you decrease then what happens? All right, what rather what will you decrease? So Joel is again on the top, Anbu and Janhvi again on the top. See guys, the minimum energy. The minimum energy required to start the photoelectric effect is called as a work function and work function is hf0. But if you increase frequency but if you increase the frequency then only you can then you only you can start the photoelectric effect. But the question said what you will decrease? Obviously you will not decrease frequency. If you decrease frequency then the photoelectric effect will not happen. In fact you can write it as hc by lambda. When you decrease lambda then the frequency increases then the photoelectric effect can start because the work function has been overcome. So decreasing the wavelength kick starts the photoelectric effect by increasing its energy lambda is in the denominator. Keep this in mind. So the question said what will you decrease? What will you decrease? Frequency can't be decreased. It will be the wavelength which will be decreased. All right. Moving on to another question coming up on your screen. Now, let's see what it is. The work function of a material is 5.3 electron volt. The stopping potential for a radiation incident is 4.2 volt. What is the energy of a quantum of incident radiation? No problem, happens Isha. Okay, let me meanwhile start to check if I can log in. Come on guys, I will do I can just I just saw it. I'm able to join in the week with guys. And why the hell did this open up? Oops, why is this opening? Okay. Yeah, I'm able to join the VQuiz guys. There is no problem. Just check it out once again. Okay, those of you are not just you need to probably log in through your account. Even if it's a free account, it is fine guys, even if it's a free account. Alright, so that's the final answers. A lot of you answered B whether it is correct or wrong. Well, looks like you guys are correct. All you need to do is just write it down in the photoelectric equation form. The energy of your photon, the energy of your photon is the work function plus E into vs the work function. is literally mentioned over here 5.3 electron volt and the stopping potential is also mentioned over here. What is the stopping potential? It is 4.2. 4.2 plus 5.3 isn't it 9.5? Isn't it 9.5e? So that's the energy of the photon. The energy of the quantum. Quantum means photon. What is energy of the photon? That's all they have asked. That's it. You got it. That's it. Cool, shall we move ahead? Alright, let's have a look at the leaderboard. Let's see who is at the top still. And literally guys, even if you are joining now, you can still participate in the WeQuiz right now. Just go to WeQuiz.in and enter this code. Wow, Joel is still maintaining his top lead. Anbu and Anthony on 2nd and 3rd. Lok Vishnu, Janhvi, Priyanka, Daljeet, Yudip and Ankit Kumar Singh. Very good guys. I'll go to the next question after the next theory pointers. Okay, let's go to the theory slides now. and see what's up in the theory slides. Okay, I think we'll have atomic structure. Yes, we do have atomic structure right away. So in this chapter of atomic structure or atoms, what you will have is the different theories by different scientists. Each one suggested a different model of the atom. Each one had its own limitations and a good thing about that theory. But the model which is fair enough to describe most of the phenomena is the Bohr's model. The first person to talk about you know the atomic structure and give a decent idea of how the atom looks like was by Thomson and then Rutherford and Chadwick then discovered neutrons and then we had the Bohr's model. So according to Thomson it was a watermelon. So imagine you know at those times in those days if you had just told that you know the atom is like a watermelon the seeds inside are basically the electrons and the red part is the positive charge and that's how an atom is everybody would have clapped hands for you everybody would hail you as a hero and your name would be over here instead of thompson that's what he said but okay not to discredit him understand even at even though the model looks very simple at those point of times you know to come up with that idea is very very difficult. Now why did he say that the seeds are like electrons and not the other way around is because they knew at that point of time is the electrons which move when you conduct electricity. So that means electrons are freely movable, it is freely movable inside that conductor. So if it is freely movable it should be easily you know you can easily eject it so that's why he thought they are like small small tiny bits. which are spread out and you can easily knock them out. That's what he thought and because an atom is electrically neutral equal amount of positive and negative charges are there so that's why atom is electrically neutral. But it failed many of the things it could not explain how spectral lines come or it could not even account for the scattering of the alpha particles when you pass it through a thin sheet of metal which was conducted by Rutherford. So then Rutherford conducted the most famous. in a scattering experiment of alpha particles and when he passed the alpha particles through a metallic surface he found that most of the alpha particles were passing undeflected onto the other side he had placed a detector around it okay so he could detect where the alpha particles are striking most of them went without you know any deviation like you can see right over here some of them got deflected by a small amount That means when the alpha particles are positively charged, remember that. That means if they got deflected slightly, that means they encountered some kind of positive charge somewhere. So the alpha particles which are positively charged encountered small amount of positive charge, that's why they got deflected. A very very few number got completely rebounded and they struck the photographic plate behind. That means... There are very few alpha particles which actually encounter that positive charge of that atom and that's when they get completely reflected back and this strike behind. That gave him the idea that since all of them are passing undeflected so atom should be most likely empty only a small part where the positive charge is concentrated. So that's when he gave this model of an atom where there is a nucleus which is heavy positively charged and electrons are revolving around it because of the centripetal force by the electric force of attraction. But even this model could not explain so many things like the spectral lines and the calculations for ionization energy and so many other things. So then after his limitations came the, oh by the way you should know all these limitations for Bohr's, they can ask you for Bohr's. Then came the Bohr's model of atom. So when Bohr gave the structure of atom, he gave it in a little bit more fancy and detailed manner and he said electrons Even though they are moving around the orbits, they still can retain their energy only in certain fixed energy levels or fixed orbits. These orbits are so special that even if a charged particle accelerates, it will not radiate energy. There is something called as Maxwell's radiation. I don't want to confuse you too much. But it says that if you take a charged particle and accelerate it, then it will emit. radiation and it will die out and it will lose all the energy but electrons even though it is charged and even though it is accelerating it does not lose energy in those special orbits those are called as the fixed orbits and when an electron jumps from low to high it absorbs energy from a light particle which is photon and if electron jumps from higher energy to lower energy it emits photons that's what he said and those fixed orbits Those fixed orbits have angular momentum which is integral multiples of h by 2 pi. Very very important this law. It has integral multiples. The angular momentum is in integral multiples of Planck's constant by 2 pi. Very very important. Okay. I hope this is clear. I hope this is clear. Okay. Now remember these postulates. From Bode's point of view, this postulate is important from your competitive exam point of view and other things are fairly simple where nucleus is at the center, the electron revolves in orbits which are stationary and these are such orbits where energy is neither destroyed or created. Only way you can transfer the energy is by absorbing a photon and shifting it to higher energy state or losing the energy in the form of a photon again. That's what it is. Now based on these postulates he was able to estimate the radius, energy, velocity, time period of an electron revolving around a nucleus and these are the formulas. You don't have to remember it like this. No, please don't remember it like this. In fact, the only thing that you should remember is what it is proportional to. Radius is proportional to n square by z. The velocity is proportional to z by n. and energy is proportional to z square by n square that is something what you should remember okay and yes the constant values what is 0.529 0.529 is the radius of the first orbit of hydrogen atom for hydrogen z is 1 n is 1 for the first orbit so that is the radius of the first orbit of a hydrogen atom that's something what you should remember then you This is the velocity of the first orbit of again hydrogen. If you put z is 1, n is 1, you will get that. And yes, there should be a minus sign over here because energies are always negative. The energies are always negative. Keep this in mind. That's the total energy of the nth orbit. Keep this in mind. All right. Now that you know this, now that you know this, yes, derivation is important for advance. Yes, Jain, it is definitely important. Now for mains and need. it is not at all important. Okay, now if you look at the energy levels right over here, you will get a sense of how the energy levels are arranged. Zero energy is for n is infinity, which makes sense. When you put infinity over here, it becomes so large that the energy becomes small, tending to zero, meaning you have freed the electron. Zero energy means it has no longer been attached or associated or bounded with the atom. Zero energy. Okay, so zero energy means it is no longer attached to the atom. It has been freed. Anything which is less it is bound to the atom. So 0 is basically free and when it is negative it is basically bound. That's why sometimes it is also called as binding energy. You would have seen that in satellites, gravitation. Keep this in mind. Alright, so you can see the spacing of lines is also not uniform because n square is there in the denominator. When n is 1, The energy is minus 13.6 electron volt and when it is 2 it is minus 3.4 volt and then as you go up and up the spacing reduces the gap is very less because there is hardly any difference when you jump from you know a very high state to a much higher state. Okay why our energy is negative? See negative energy means it is relative to the highest energy which is when it is free. So imagine I tell you the energy is minus 13.6. Okay, electron volt. If it is minus, it is relative to this. If you want to make this electron jump from here to here, you need to supply energy and the reference is assumed to be zero at infinity. Just like for gravitational electrostatics, you say that when the particles are infinitely apart, that's when their energy is zero. That's a reference energy. Like for MGH, you always take some reference, maybe the ground level. So here the reference is infinity and that's where you have assumed it to be zero. So if you have to supply energy to reach zero, if you need to give energy to reach zero, that means your energy right now must be negative. I hope this is clear. Okay, understood. All right. Let's talk about the last part in this which is called as your hydrogen spectrum. And you get amazing, you know lines. or spectral lines which come out of you know different elements which are like its signature you also have your own signature right you also have your own signature so even elements have their own unique signature which does not match with any other element that's called a spectral lines now why does it come is because when you agitate and when you give energy to the atoms they start You know, woggling, they start shaking, they hit each other, they transfer the energy and when they hit each other because of their temperature, they knock out electrons and these electrons can then shift to higher energy states. So, the temperature gives the thermal energy which can then knock out and which can supply energies to the electrons during the collisions. When the electrons go to higher energy states, they will not be happy for a long time. They will want to come back. Like, why are you sending me up? I want to go down. So they will eventually come down. When they come down, they are going from higher energy state to lower energy state. That's when you will see photons will be emitted. That's when you will see light will be created. Depending on which orbit to which orbit they are jumping, their energy difference goes in creating that photon. So that's why each jump corresponds to a specific energy which also corresponds to a specific frequency of that photon. So that's why you will see some unique lines depending on their jumps from higher energy to lower energy. That's why you see this unique signature out here. Is that clear my warriors? Is that understood my warriors? That's very important. And yes you have your Lyman, yes Ankit you have your Lyman Balmer Paschen series depending on the jumps. If you jump from any energy state apart from 1 to n is equal to 1 that's Lyman. If you jump from higher energies to n is equal to 2 you have Balmer and then if you jump from higher energy to the lower energy which is 3 then you call it as Paschen series. So these jumps have been classified depending on where their final destination is final destination is one Lyman two Balmer three passion then bracket p fund that's how it is that's how it is clear okay now I'll just write down few equations the energy difference between you know the states or basically the orbits the orbits goes into the energy of that photon which has been created you So that will be hc by lambda. Now when you solve this further by substituting the formula of energy of you know the electron in different states. You get this relationship 1 by lambda is R z square into 1 by n1 square minus 1 by n2 square. Very very important formula if you want to calculate the wavelength between two jumps. n1 and n2 are your initial and final destinations of the electron between the jumps. R is called as Rydberg's constant, z is your atomic number. So that's how it is. Oh why is it named like this? It's named based on who discovered it. That's all Ankit. Okay let's start with some quiz which is going to come up on your screen and here it comes. Let's start that quiz. Yep the question should be up on your screen in three, two, one, now get ready. Okay so here we come with the next question is Bohr's model of atom. assumes Boards model of atom assumes which of the following the options will be visible on your screen in a bit train man sir if my home state NIT does not have home state OBC quota and I have filled the form in OBC so will I be allotted general category home state or national you'll be allotted general category home state train man not national obviously they will always give preference to your home state and then comes national is that okay train man The nucleus is of infinite mass and is at rest. Electron is a quantized orbit, will not radiate energy and mass of the electron remains constant all of the above conditions. Guys this should not be infinite this should be finite okay this is not infinite just make it finite okay and is at rest okay and electrons is in a quantized even if you take it as infinite still it will be Okay, I'll tell you why in a bit because anyways the time is up. Okay, so guys the correct answer is all of the above. Yes, most of you are correct. Strictly speaking, the nucleus has a finite mass but even if you make the assumption that is infinite mass it works because I'll tell you why. If the mass of the nucleus, if the mass of the nucleus is finite and if the electron goes around it, actually speaking even the nucleus should go around. nuclear should go around because their center of mass should stay at rest. Remember when two particles go around each other because of their mutual force of attraction, they always do so around their common center of mass. Now if you don't want the heavier particle to move like when the earth goes around the sun, we assume the sun is at rest but technically sun is not at rest, sun also wobbles around. So, We make the assumption that the Sun is rest that means it is very very heavy it's very very heavy and that will make sure that the center of mass lies on the Sun. Same way the center of mass of the nucleus and electron is on the nucleus then the nucleus will not wobble it will stay there. So that can only happen if it is infinite but actually speaking it should be finite. I hope this is fine. Next the electrons is in quantized form yes the energies are always fixed and only in those quantized energy states it will not radiate energy. Mass of the electron remains constant, yes it always remains constant, it never decreases or increases. Perfect, let's see the leaderboard right now. Okay great, so we have Joel still on the top, Anthony still leading, Anbu Raj, very good Priyanka, sorry VLog, Kaushik, we have a new person, Janhvi, Manojnya and Dalijan. Wow, we have some new names coming up on the leaderboard. Next question on your screen now. Here it comes. Here it comes. The ratio of radar of the atom assuming Bohr's model A is, come on, let's see how many of you can get this. The ratio of the radar of the atom assuming Bohr's model A is, it's going to be an interesting one. Okay, here are your options. You can start working it out. You have one minute to answer this question. I'll give you a hint. Think about the radius formula. Think about the radius formula, bachalok. Okay, think, think, think. Okay, SSM, you study well, but I'm not getting, but I, well, I study well, but I don't, I am getting fear while studying how to overcome this. SSM, most likely it's the. fear which is coming out because you have not practiced enough pyqs so once you get a strong hold of pyqs that fear will go away so start with mock test start with some more good questions and Slowly start doing the PYQs without seeing the solutions or answer ki. You will slowly overcome the fear bacha. Okay, let's have a look at the final answer in 10 seconds. Ankit, it should be showing. I'm not sure why it is not showing. It should be. Mohan, watch this one shots. Also watch my regular classes. It's there on YouTube also in the 12 standard pathfinder. It's there. The playlist series is there. Watch the modern physics classes. It will take you 2 to 3 days max. Within 2 to 3 days, you will become an expert. Okay, just do that. Let's have a look at the results. And looks like many of you are wrong. I'll tell you how to do this question. You need to see how many shells are there. Remember, the radius, the radius is proportional to n square. Now if you look at this atom, don't look at the atomic mass number, look at the atomic number, which is 13. So 13 will be nothing but 2, 8 and 3. So there are basically 3 shells. Similarly, when you write for 52, 2, 8, 18, see how many shells will come. I think there will be 5 shells coming out over here. So when you take the ratio of the radii, R1 by R2, which will be N1 by N2, whole square it will be 3 by 5 whole square so 3 by 5 whole square is 9 by 25 that's the answer pyq can be asked in different ways in need bacha not directly they will not repeat but they can change the values or just they can change what is given can be asked and what was asked can be given they can change all these things all right so let's have a look at the leaderboard some of you are really maintaining your stand Very good Joel Anthony Anburaj. Excellent day. And here comes the final question on your screen. Now, here it is. Very good Anthony. That is very good. How 5 shells Ankit? Just write the atomic structure of it. K, L, M, N. Ankit, you know right? 2, 8, 18. Check it out. How many shells will come? You will get 5 shells. Yes, yes ZenBod, I will be doing one shots for 11th portions also but first preference for 12th term too because that is coming very soon. Okay, cool. So the ground state energy of hydrogen atom is this much. When the electron is in the first excited state for helium then the excitation energy is. It's for helium, be careful. Is NCRT alone enough for modern physics? Mohan? 90% yes, 10% maybe you might need some help, 10-15% from HC Varma. Because there could be some questions which require some good level of understanding and concepts and that I feel you will get it from HC Varma. If you want to score 120 marks or 130 marks in physics then not needed. But if you are aiming for 120+, 140+, in physics then you need to study from HC Varma. Okay, Pathfinder is available for an entire timer. It is now called as 12 standard. 12 standard J neat. You will see it 12 standard J neat. You will see it physics, chemistry, maths, everything has been arranged. All right, let's have a look at the results. The correct answer. Oh, very few people got it. I'll tell you what you have missed. This is the energy of hydrogen. But what is asked is helium. They are completely different. And it's excitation energy has been asked. So to excite it means you have to go make it go from one to two. So the energy difference that we are talking about here is E1 minus E2 modulus of that. So basically it will be 13.6 that's constant value. Z for helium, Z for helium is two. So you will have Z square, which is two square by you know one square minus Z square. by 2 square this is what you're going to get just do the math 2 square is 4 and here you will get 1 so just do the math guys you're going to get the final answer z square by n square just do the math and you will get the answer yep so it should be it should be yeah it's not 3.5 it's helium it's not hydrogen be careful about it be careful okay just be little bit careful about it Alright, let's have a look at the final leaderboard. And let's see how many of you got it. NCRT alone. enough for modern physics no mohan like i said for getting decent marks yes would you get top marks no okay so it should be working bacha if it is not working then i'll tell you what to do and yes we have our winner for today joel very good anthony very good yuvadeep very good congratulations bachalok you have done fabulous job out here you've got very good marks proud of you i'll just end the quiz right now so All you need to do is if you're watching the video right now and if you're still not able to join the telegram channel I'll tell you what you can do. One simple hack usually which works. So telegram channel just click on this. It is not working. Okay you see this link over here in over here that t.me right just replace it with telegram just replace it with telegram and let put that enter button now you will be able to join it that's the only thing or change that you need to do that's it guys all right perfecto let's move to the last thing yep so guys if you enjoyed the session make sure you go ahead join the telegram channel so that you get all the important updates go ahead hit the like and subscribe button and yes all those interested in the crash courses go check out the link which is there in the description box Because crash courses are available for a very cheap rate of just 1800 rupees. Go ahead, check it out. All tests, assignments, lectures, recordings, everything is available just for you, both for GE and NEET. All right. Thank you very much for tuning in. And I hope you guys had a great time. Bye bye. Take care. And yeah, the crash course validity is till the last exam, even if it gets postponed. Don't worry about it. Bye bye. That's it from my side. This was Shreyas here signing off.

Neelarjanan, hello, good evening. So, those of you who do not know me, my name is Onion, oh sorry, not that Onion, my name is Shreyas and I am the physics master teacher and I have been doing lots of things, you can read it out here, blah, blah, blah, blah, blah and you can also follow me on Instagram. Okay, cool.

So, let's get started and yes, we are going to see. A lot of things today, dual nature, photons, properties, photoelectric effect, Thoms and Slutdorff model, Bohr's model, hydrogen spectrum, all of this in today's one shot just like Anian said. Yes, Sundar, oh my god, my secret is out. Okay, it's not a secret actually.

Anian, actually the spelling of onion is not O-N that Kanda, no, no, it's something else. A I think, A-N-I-Y-A-N, okay. Cool!

Dual, dual means Ankit this is dual. See this, this is dual. This, you are this and then that, that's dual.

This is one, okay so that's one and what you see behind that one that's dual. You have some personality this side, some personality the other side. So that's dual. You have a dual personality disorder.

So that's what it is. Alright, cool. So, In the first part of this session let's talk about the dual nature of light like I just told you. Light sometimes shows particle like behavior as in it shows properties like momentum, force just like when you throw a ball on somebody's face. Have you thrown a ball on somebody?

Please don't do that. Okay so obviously you will get hurt. It has some momentum it will exert some force and if you throw balls you know through an opening the ball will pass through the opening without getting deflected. straight ahead of that opening. It won't bend just like Rajnikanth does when he shoots bullets from his gun.

The bullets bend, that's weird because the bullets are particles but that's Rajnikanth again. So that's an exception. And it also shows properties like interference. It also shows properties like diffraction, refraction.

All these are the properties of waves. So we have associated dual nature for light. It's like okay you exist together, no problem. we have no issues whatsoever yep is this complete section yes ribaka definitely good evening chandra leka wow i like your names guys amazing names nilarjan such powerful names anurag joseph samrat look at the name mansa ready my god chandra leka vandana alw crazy anthony gerard vignesh rasuri amazing names you guys have proud of you okay so according to einstein The particle nature of light what is it called?

Photon. Photo? Photon. Okay. So a photon is like a packet of energy which carries energy and these packets travel very fast at the speed of light and these packets when they hit something when they interact with other matter they transfer their momentum to that particle they create an impact they create an impulse ok and each packet like I told you it has photon which is called as a photon has some energy I'll give you that energy formula and all the important details about the photon these are the most important properties which you should know you know from the theory point of view for board exams also from neat point of view.

So photon always travels at 3 lakh kilometers per second or 3 into 10 to the power 8 meters per second in vacuum and it doesn't matter how you see the photon. So that's very weird but you know it's true that no matter how fast you travel you will always find the photon traveling at 3 lakh kilometers per second. Okay now the energy of the photon is given by this formula.

I'll just put it up right over here. The energy is given by the energy of your photon is given by h into f. But we all know the speed of light is frequency into the wavelength.

So frequency can be replaced by c by lambda. So you can also write it as h c divided by lambda. This works.

All right. Very good. The week we will start in a minute.

Just hold on for some time. Yes. And the photon is the energy particle so it has no meaning at rest.

The rest mass is zero. So when you see a photon at rest that means something impossible has happened. You can never see the photon at rest because the photon always travels at 3 lakh kilometers per second. Even if you travel very fast photon will appear to travel even faster.

So you know it's always constant so you can never see the rest mass but it has been assumed to be zero. So, lot of people think, sir, the mass is zero, sir. Then, the momentum will also be zero.

That's the funny part about photon. This is a very fascinating chapter. You think this, this should not happen, but that will happen.

You think that should not happen, that will happen. So, mass is zero, but it still has momentum. Photons are neutral and stable.

They won't decompose. They won't combine together to form new things like atoms do, like they split or they combine to form molecules. and they get and they do not get deflected by electric or magnetic fields, which is obvious because it does not have a charge. Now, the rest mark is zero, but it has momentum, but it has momentum.

And what is the momentum of a photon, the momentum is H by lambda, that's very, very important, you should know this. And if you take this, P and substitute it over here. You can see H by lambda is right over here, right?

H by lambda is right over here. You can definitely write it in terms of momentum as well. Yeah, momentum is E by C, you can substitute all these things up to you. Yes, expectation and reality not equal to. Can I start class 12 with modern physics?

Not a good or a great idea, Ayesha. You should start it probably with other chapters. Okay. But yes, if you are in NEET 2022 or JEE 2022, yes, you can start.

But if you are 11th to 12th moving, then don't start. Okay, great. Now, there is another concept which is called as the radiation pressure or the radiation force.

So when light falls on your face or when light hits something, it applies a force. That force is small, but it is still there. And we can find that force out depending on whether the object or the surface on which it is falling is an absorber or whether it is a reflector. So if light falls on a surface which is absorbing in nature it falls and it gets absorbed then the change in the momentum then the change in the momentum is final momentum minus initial momentum that's it and you can calculate and you can calculate This momentum, okay, magnitude wise, you all know, it is nothing but, you know, h divided by lambda, that's it. It's nothing but h divided by lambda, that's the wavelength of this light.

But if, if the surface is reflective in nature, it will change its momentum in the opposite direction. In that case, the final momentum change or the momentum change will be final momentum minus initial momentum. So magnitude wise you are going to see that the final momentum is exactly negative of initial momentum.

So that's the reason why you will have minus pi minus pi but you're taking the mod so it will be basically two times the initial momentum or two times of h by lambda. Is that right? Everybody got it?

Yes. Excellent. Very very important. Now also I'll give you one more important formula which you should know. If light is falling on a surface and it has an intensity p.

It has an intensity of I. What is the meaning of intensity? Intensity means how many watts of energy is falling per unit area.

How much is the energy which is falling per unit time per unit area. That is intensity. If the intensity is given then on any surface which has some area A, the pressure. The pressure which is also called as the radiation pressure is given by I by C.

I by C, intensity by speed of light and the force because force is pressure into area. It will be nothing but I by C, the whole into A. So the force on that surface will be I A by C and the pressure obviously will be I by C.

This is if it is absorbing. This is if it is absorbing. Okay, if it is absorbing, if it is reflecting, what will you do guys?

What will you do? What will you do? Come on quickly tell me you should be able to tell me this.

What will you do if it is reflecting in nature? What will you do if it is reflecting in nature? This is absorbing. So that's why it is IAYC. But what will you do if it is reflecting in nature?

If it is reflecting in nature, you are just going to multiply it by two. That's all. That's the change.

Yeah. 2i by c perfecto great now let's move ahead and here comes another interesting hypothesis given by de broglie so light shows wave and particle wave is when it goes and interferes young's double slit experiment particle that's the photon nature which it has momentum force pressure all of those things even matter like us electrons protons you They also have dual nature. Usually your particles around you show particle behavior. Your bottle shows particle behavior.

But in a very microscopic level, at a very quantum level, when you zoom in, things look very different and it can show wave-like properties. So for a particle of mass m moving, Moving with momentum moving with momentum. Okay, P the matter wave the matter wave the matter wave is the wave associated with a particle not with a photon.

It is not an electromagnetic wave. It is not a sound wave. It is not a wave on a string. It's not an earthquake. It's a different kind of wave which is not possible for you to visualize or see through your naked eye.

The matter waves, the matter waves wavelength, wavelength which is also called as the de Broglie wavelength is given by h by p. If you notice this formula is very much similar to the previous formula. I'll show you over here.

P is h by lambda. Just shift lambda there, put p down. You will get the de Broglie wavelength for a matter wave.

That's it. As simple as that. Yes, you would have learned this in chemistry.

Very good. Excellent. Yep. Now, once you know this, you can also substitute momentum as terms of energy like this.

The kinetic energy of a particle, the kinetic energy of a particle k will be half m velocity square, which is also the momentum square by 2m. You can substitute momentum as mv, you will get the same expression as before. Hence from this momentum will become 2mk but that's the square of the momentum so momentum will be the root of this.

You can even substitute it over there and this will be nothing but h by root of 2mk. This is only for particles of matter mass something which has mass like electron proton bottle pen my hand you watch air everything so that's when you will use this formula but when you are talking about light or electromagnetic waves then this is the energy formula you will use or this is the momentum formula that you will use. Are you getting the difference?

Light is an electromagnetic wave. Electric field, magnetic field, completely different. The particle nature of light is called as photon whereas the general particles around you electrons, protons, neutrons they have a mass m, kinetic energy k. And their matter wave which is completely a new kind of a wave like sound wave, wave on a string that is having a wavelength of h by p.

P is the momentum of that particle. Completely different. Okay time to join the week quiz using the code 224283. It should be also pinned in your chat box. I have also shared it on the telegram channel and another way. is going to the description box and then joining it using the link and another way is just going to vedantu.com slash v quiz and entering this code that's it either ways you will be able to do it yes free car i will do it okay so come on guys start joining the class right away and i'll be starting the v quiz in no time okay so go to www.vquiz.in and use the code 224 283 or you can directly click the link which is there in the chat box and then you can start.

Alright come on guys waiting for all of you to join go ahead and start joining the V quiz right away because it's going to be fun and throughout the session we are going to have V quiz after every theory concept that I'm going to teach hopefully the V quiz works today. No Ankit there is more theory because there are more topics as well come on I'm going to start the first question Usually you will get 45 seconds. Some questions towards the end will have around 60 seconds.

Alright, are you guys battle ready? Okay, are you guys battle ready? Okay, come on, come on, come on, come on my warriors. Join in. This is Kavya for 12th standard students.

But if you are 11th standard student, you can still join in. Because you would have definitely studied this in chemistry. Definitely.

Hello, Hare Krishna. Welcome. Hi, Janhvi.

Hello, Rama. Hello, Reshma. Hello.

Welcome, welcome, come on join in, join in Ankit, join in Srikar, come on. Alright, one minute, I'm going to start, within one minute I'm going to start. Alright, so get up, we have decent number of people and I'm going to start any moment. Oh by the way, let me also tell you, even if you are watching this session recorded, you can still join the VQuiz, although you might not come in the leaderboard, but you will still get points and you can compare yourself with the students who participated live. That's a very cool feature of V quiz and that's how you can even participate in all the class quizzes even after the live class is over.

But yes, the fun of a live class is completely different. All your attention on the screen. I'm starting the quiz in 3, 2, 1, go. Here is the first question on your screen now.

Yep, I've started. Can be, Harchini this is a Neat Channel plus J channel. Yes, you can definitely use Harshini for NEET.

Exactly, this is for NEET. Please read the description box guys. When a high-energy UV photon beam enters the electric field, it will be?

Come on, this is an easy peasy lemon squeezy question. Accelerated, retarded, undeflected, none of these. Okay, make sure you write or post answers only in the week with nowhere else.

So come on, an introductory warm-up question for all of you just to brush up your concepts. Today's lecture is all about concept revision and formula applications. Okay, Ara not here, you have to go to vquiz.in, Ara Vindhan, go to vquiz.in and enter the code and participate there.

Malik, Moni, go to vquiz, not here. Okay, time is running out in hardly 10 seconds. Divya, not here, not here, go to vquiz, go to vquiz, participate there, that's the fun.

There is no fun here. Alright, so let's have a look. I would request the admin to block the students who are going to put the answers over here. Okay, so accelerated wow and undeflected thank God. Yep, that's the answer guys.

How will it be? Okay, let's see the result. Okay, so look at this guys.

So many of you answered it wrong. Why will it be accelerated? A photon is a charge less particle and when you pass it through electric or magnetic field it has no effect on it. because there is no charge there is no north pole or south pole so hence there will be no change in its velocity Good evening Alpha. Okay, so let's have a look at the leaderboard.

Who is this? Anuraj, Rosh and Dalijan. Very good, Janhvi.

Very good, Joel, Dhruv, Srilata, Priyanka, Yuva Deep and Parithi. Excellent. Moving on to the next question. Get ready on your screen now.

Question number two. Let's see how many of you can answer this. A radiation of energy E falls normally on a perfectly absorbing surface.

The momentum transferred to the surface is which of the following options? Okay, come on my warriors figure this out if energy Falling if the radiation of energy e is falling on a perfectly absorbing surface Then the momentum transferred is e by c to e by c e c e by 2 c Interesting. Yes alpha you can definitely join in there is nothing that you have lost. Okay, join in go ahead and participate You will have fun. Even if you are watching the video right now, is it e by c?

Is it 2 e by c? Is it e c or e by 2 c? okay let's see how many of you can answer this question 24 seconds this is straightforward direct come on I want you to fight it out but the catch is who will answer it very quickly all right and the time is going to be up in five four three two one and showdown I guess Yes, some more theory, yes Ankit, lot of theory to come. Yes, definitely, definitely.

Let's have a look at the results and this is how our students have answered. Some of you have answered E by 2C, E by, E C also, 2E by C also and E by C. Oh, okay. Perfectly absorbing surface, the momentum transferred, actually it should be A not B. This is wrong, this should be correct.

Oops, sorry guys. I think somebody who made the quiz. gave a wrong answer over here it should have been E by C if it was to E by C it should be reflecting surface so I'm not going to show the leaderboard let's just skip to the next question it should be E by C E by C okay I mean if you look at it this way also look at it this way that the perfectly absorbing surface then the momentum transferred so if it is getting absorbed then the change is only E by P But if it is getting reflected, if it is getting reflected, then the change in momentum will be 2p.

So the two factor comes only in case of reflecting. Yes. Okay.

So let's just move ahead to the next question coming up on your screen. I'm not going to show the leaderboard. Question three on your screen now. Okay. So Sri Harshit, you got Ekalavya.

Proud of you. Make the best use of it. And you're going to rock it. Hope to see you soon. during the victory celebration when you crack J advanced.

Okay, if the kinetic energy of an electron is made four times then the de Broglie wavelength will then the de Broglie wavelength will come on come on come on come on. Okay, come on. Let's see how many of you can get this. Okay, come on, come on, come on, guys.

Let's see how many of you can get this. What is this? Oh my god!

Eeeh! Hari! What do you mean by that man? If the kinetic energy of an electron is made 4 times, then what do you think is the de Broglie wavelength?

What do you think is the de Broglie wavelength going to be? Come on! Come on!

No, no, no! Don't answer over here. Don't answer over here.

Try to answer in the V-Quiz itself. I wanted you to participate in the V-Quiz to get a feel of your mock test or your actual examinations. Alright!

Let's have a look! How many of you got the correct answer? Wow, very good, very good, very good, very good. See guys, what happens is if the kinetic energy of an electron is made four times, then what will happen to the wavelength?

De Broglie wavelength is your energy, okay? I'll just put it like this. De Broglie wavelength, De Broglie wavelength is h by p and your momentum is root of 2mk.

isn't it? Root of 2mk. I just gave you that formula.

If you notice over here, this kinetic energy will become 4 times but it is under the root. So, root of 4 is 2 and it is in the denominator. So, hence this wavelength will become 1 by 2 times and 1 by 2 times means it will decrease by 2 times. That's it.

That's all you have to think about. Okay, just use the formula. That's it. Alright, let's have a look at the leaderboard now and see what the scores are looking like and then we will go to the theory part. Wow, we have Abu Raj still at the top, 2939 points.

Joel, Janhvi, Anthony, Srilata, Ankit, Harish, Abhinash, Rosh and Kavya. Very good, Bacha Log. I will not show you the next question because the next question will come after some time because we have to go with the theory part now. Alright, so let's go to the theory of the next topic and that is the photoelectric effect.

See, we just talked about how light can behave both like a wave as well as particle and normal matter can also show wave-like characteristics whose formula is given by de Broglie. Now based on the concept of photons, The photoelectric effect can be explained. Photoelectric effect is nothing but when light of sufficiently high energy falls on a surface then electrons are ejected out and if the electrons are collected and you connect it across a circuit you will see a current which is established in the circuit. This phenomena where electrons get ejected out because of high energy light that is called as photoelectric effect okay the electrons which are ejected out they are called as photo electrons photo means light so electrons ejected because of light are called as photo electrons number two number three because the electrons go to the other side and they will start moving around in the circuit so there is a current that current is because of light again hence what will it be called Photo current as simple as that.

I hope this is clear. Yes, I do remember Rohit Kolthai. Yes, definitely.

Now, now ejected means it is thrown out. It has been ejected like you would have seen some movies or maybe some documentary where there is a pilot and because of some malfunction in the plane, the pilot ejects out of the plane. He's thrown out of the plane, okay, by himself.

So, that is what is ejection basically. Okay, now what happens is we need to understand the different parameters related to frequency, intensity, is there a relationship with the current and can I somehow increase the current by connecting a battery or reversing the polarities. Also what will be happening if I change the plate over here, will there be any effect on the current or other things. This plate is usually metallic in nature because what is the speciality of metals.

They have free easily ejectable electrons. Things like plastic or wood, they have electrons but it is very difficult to knock the electrons out. So usually you will use a metallic surface where you have easily removable electrons so that a photo current can be established.

Great. Next, so let's talk about all the important aspects about you know photoelectric effect one by one. So You should remember this setup always.

You will always see the light will be falling on one side, photoelectrons will be ejected from that side and they will be collected and they will be establishing a current in the circuit because if the electrons go like this then actually the current will be going the other way around. Just keep this diagram in mind. We are going to solve a lot of problems.

Now why should the light be of a sufficient wavelength? or a certain energy. Okay. See whenever there is a free electron inside the metallic surface it's not truly free.

It's not exactly you know free in the sense you do not need any energy to take it away. You need to pay some tax. You need to pay some commission to take out that electron because that electron is still slightly bound to the atom inside that metallic surface. So, if you notice these are different colors of light and you would notice this is red, this is green, this is violet and in red color light when it is falling on the surface there is no electron which is coming out but in green yes you have in violet or blue you have some electrons coming out.

What is the reason for this? Red has a very less frequency or large wavelength. Hence the energy is less. The energy of photon is less.

But in the case of green photon, the energy is more. In case of violet, the energy is even higher. So therefore, you would now realize that there is a critical frequency for which the photoelectric effect will occur. After that, below that frequency, you will not see the photoelectric effect occur because the photons do not possess that energy to knock that electron out.

Okay, it does not have sufficient energy to knock that electron out. Okay, so that energy, okay, that energy which is required or that frequency which is required to knock that electron out is called as the threshold frequency. What is it called? It is called as the threshold frequency because that is the frequency only after that you will see photoelectric effect which will occur. That is generally denoted by the symbol f naught.

and photoelectric effect, photoelectric effect occurs if f more than f0. If f is less than f0, it will definitely not occur. Now, what is the relationship of this frequency with some other parameters of the entire photoelectric setup?

How do you think this F0 is decided? What is that thing which affects F0? Who decides the value of F0? Can you guess? Can you guess?

Think about it. Critical means that's the minimum frequency after which the effect will occur. Remember the energy of a photon energy of a photon is HF blue light Violet light has very small wavelength, high frequency.

So more energy. Red light, large wavelength like you can see. So less energy because less frequency. So that's the reason why I said more the energy of the photon, the good that better the chances is for the effect to occur. And the minimum critical, that's the limiting.

He's in the critical stage, meaning you do not know what is happening. Okay, what can happen? So after that only, You can decide okay if effect is going to occur or if the photoelectric effect is not going to occur.

Yes, I hope Girishma, Janhvi, all of you have understood it. Kavya, everyone. Hello Mahesh. Welcome. Yep.

Is this clear? Yes, I'm going to come to photoelectric equation also. Now that critical frequency, the frequency required to throw out that electron depends or that critical frequency required to start that effect depends completely on this metal.

See, imagine you are holding something which you like. What do you like guys? Maybe you like ice cream, maybe you like chocolate.

You are the atom. You like your toy, maybe a teddy bear or maybe a chocolate. You're holding onto it.

Okay, I'm just going to imagine I love this bottle. or I love what is in it, maybe it has some very nice mango juice or lime juice, I don't know, whatever, I'm going to hold on to it. Somebody comes with very high energy and he knocks me out and he takes it away, he takes it away. If that somebody coming from that side has very little energy then I will not give it to him.

If he comes from that side and he tries to take it, I will hold on to it. If somebody with very high energy comes, There's a very good chance he can knock it out and take it from me, snatch it from me. Now imagine I am little bit stronger or I am little bit weaker.

If I'm weak, I hardly have a grip on this like this, then the person comes from that side, he will snatch it away very easily. So the minimum energy required for snatching that or ejecting that electron depends on the metallic surface. Understood guys?

Somebody saying laptop. Hi Agadish. Very good. Very good.

Excellent. Nature of the metal. So this F0 depends completely on the metal surface and that minimum energy required, that minimum or critical or critical energy required. What is that minimum or critical energy required called? That is called as your work function.

What is it called? It is called as your work function and that will be equal to HF0 which is the energy of the photon obviously. That energy of the photon which is needed to just throw out that electron is called as the work function.

Very good. All right moving on. This work function like I told you it depends from a metal to a metal.

to the next metal like gold might have different work function, aluminum might have different work function. As a minimum quantity of energy required to remove an electron. Okay to completely eject out that electron.

Okay. I hope all these definitions are very very clear. Excellent.

Now, let's talk about the next part and that will come over here. Here right now there was no battery but imagine there is a battery. Okay, let's try to understand.

See these electrons which are ejected the electrons go like this and follow this path that means the current which is established in the circuit will be exactly in the opposite direction. This is how. The current is established.

This is how the current will flow in the circuit. If somehow you place a battery, you place a battery and you push the current or you help the current, more current will flow. Like for example, if you place positive terminal here, negative terminal here, what will the positive terminal do guys?

What will the positive terminal do? It will pull more electrons. It will happily pull more electrons.

that will increase the current. More current will flow obviously but if you connect the battery to oppose the current, if you connect the battery in the opposite manner then the current will decrease and that's what I want you to see in the next GIF and animation. Observe this, observe this.

Look at this, in this situation the light is falling, light is falling, electrons are ejected and slowly you are changing the current. slowly you are changing the current and how are you changing the current by increasing the voltage look at this 1 volt 2 volt 3 volt so when you increase the voltage what happens is that the positive terminal is connected here positive will pull more and more electrons so the current will increase naturally it will increase yes work function is energy go cool threshold frequency is hertz frequency. Phi is HF0 and they both are related more frequency threshold frequency more work function but one is energy one is frequency units are different there are two different physical quantities go cool.

I hope this is clear. Next important thing that you should realize that if you reverse it like over here you can see that when you increase the reverse voltage the electrons which are ejected out feel resistance to reach here because now the negative terminal is connected here. Negative, negative repels. So you will see the electrons which are reaching now face a lot of difficulty and there could be a potential, there could be a potential for which, for which the electrons are no longer able to reach here.

The potential or there is a voltage for which when you increase the voltage after that, there is no further reaching of electrons to the other side. That reverse voltage for which you stop the flow of electrons is called as the stopping potential. Electrons are ejected out.

Okay, electrons are ejected out and you are like stop it or stopping it by creating reverse voltage. So that minimum voltage for which the electrons stop is called as the stopping voltage or stopping potential. I hope this is clear.

And that minimum energy. that energy minimum to stop to stop the photo photo electrons. We all know we all know that the voltage difference applied to a charge causes acceleration or deceleration.

Here it is causing deceleration. So voltage difference of V volts to a charge of the electron which is E causes an energy difference of how much charge into voltage. Remember this formula. This is standard. This is in electrostatics.

The energy due to the energy due to acceleration or deceleration is nothing but the charge into potential difference. Do you know this formula? In case you have forgotten now remember it.

Energy difference is charge into voltage. So that minimum energy which is required to stop it, so you have changed the energy of that electron so that energy required to decelerate it will be the charge of the electron into the potential difference which is Vs. This Vs is your stopping potential, stopping potential or stopping voltage difference. Is that clear?

Yeah, it's something like a capacitor but in capacitor the electrons don't move between the plates, they move from the outside part. Here the electrons are moving between the plates in that area. Empty space.

EMI for this part? No. Yep.

Yes, it could be. It could be mixed with magnetism as well. Yep. All right. So, be stable.

I'm teaching in the 12th standard batch, 11th to 12th moving batch, also in the crash course, which is for the 2022 students. Okay, fair enough. Now, let's come to the main part, which is the Einstein's equation. Einstein's equation. A lot of people get confused, I don't remember, sir.

How to remember? Please help me. I will help you out.

You make it like a story. I just told you what do you love guys? It could be laptop, it could be Dairy Mill silk, it could be bottle, it could be teddy bear, it could be anything. Okay, you're holding on to it. Some person comes with a lot of energy snatches it away.

When you are resisting, you are sucking away some energy from him because he's going to knock you out and you're going to resist. He might come with a lot of energy but while resisting he will lose some energy because you are going to make an effort to not lose it. But anyways he snatches it and the precious thing goes away.

So he will have little he just took away this bottle now this bottle will fly off okay but it will have some less energy. Same thing happens here look at this now look at this light is falling on an atom of the metallic surface it knocks out that electron and the rest of the energy is used as kinetic energy. So what happens is that the energy of the photon goes in knocking it out, knocking it out, knocking or basically ejecting it out and the rest of the energy is the kinetic energy of the electron which has been ejected. So, what is the energy of the photon guys?

It is HF, isn't it? It is HF. What is the energy required to knock it out or eject it? It is the work function. And what is the kinetic energy of the electron?

Well, I'll just put it as Ke. That's it. So this is your basic, you know, or the most elementary level of writing the Einstein's photoelectric equation. The photon's energy goes in rejecting it and the remaining goes as kinetic energy.

Now I just told you the formula for phi. Don't forget it. What was the formula for phi? It was nothing but HF0, isn't it? Work function, the minimum energy required.

happens at the threshold frequency minimum frequency that is hf0 okay is the energy now kinetic energy how do you measure the kinetic energy of the electrons the kinetic energy is measured by this formula evs tvs is the energy required to stop it that's the least energy you require to stop it after that you will never see the photoelectric effect because it will not come to the other side you will not see current sorry you will not see current into that circuit so you're absorbing all the kinetic energy of the electrons it came with full josh it came with full josh and then you stopped it and it went back so you're absorbing that kinetic energy hence the kinetic this measures this whole thing measures okay the kinetic energy of the electron and hence i can just write this as E into Vs this becomes your more advanced version of writing the same equation. I hope this is clear. No crash course lectures you know are still available for you to view it as a recording in case you had joined before but if you are planning to join now then you can still join and watch all the lectures you can also give the test at your free time. Okay so both the equations are very easy.

Very important. Is that clear? Can we move ahead to some more questions? Also notice one more thing intensity has no role to play in all of this except for the fact that if the light is more intense if the light is more intense if I can put if light if the light is intense then I can put a light on the other side of the screen.

There are, there are more photons. Then there are more photons. If there are more photons, what does it mean?

More photons will eject more electrons. So there will be more, there will be more photoelectrons, more photoelectrons. If there are more photoelectrons, what will happen?

The current in the circuit will also increase. Keep this in mind. very good okay great no Jayant I do not teach good in crash course I teach very bad I teach only good in some places why will I teach good in crash course what is there no obviously I don't teach okay so let's go ahead to the next quiz coming up on your screen so what is K max equal to Aishwarya K max is exactly this the max kinetic energy of the electron you have absorbed it why max kinetic energy why all electrons have different kinetic energy because they will have trouble getting out some electrons will have lot of trouble to get out of this plate some electrons will have less trouble.

The electrons which have less trouble getting out they will have more kinetic energy so stopping them will be more difficult. Understood? If electron has less difficulty to come out it will come with a lot of energy so we'll have more difficulty to stop it.

So hence the maximum kinetic energy is measured by you know measuring the stopping voltage. So the last most luckiest most energetic electron if you are able to stop it, then for sure you have stopped every other electron. Okay. And yes, some students were like, Sir, what's the what about the graphs? Well, I can show you certain graphs like this, this one very, very important graph, like this one over here, the current versus the voltage.

And if you look at the current versus the voltage graph, the graph will look something like this. This is your negative stopping voltage. This is zero volts.

This is your positive voltages. The current increases and it saturates. It saturates at a point.

It saturates. Why? Because after a point all the electrons are ejected.

How many more will you eject? There are only a limited number of electrons. So you can only emit or you know, emit electrons as many as you know photons are falling onto it.

If 10 photons are falling, 10 electrons will eject. So beyond that you cannot increase it. And if you increase the intensity, and if you increase the intensity, then what happens? If you increase the intensity, then you will see the graph go up. This is for more intensity, which I just told you.

When intensity increases, then the current also proportionately increases. This is for more intense light. This is for more intense light, which is very, very important.

You should know this. Jayant, we teach the same way or you can say, you know the teaching style could be different but we put in our 100%, 200% efforts both on YouTube. YouTube teaching is different because this is on this big screen and you know the kind of interaction we have is different. In crash courses or on the Vedantu platform, we have another teacher to help you out.

There are lots of quizzes and there are leaderboards and so many other things that happen. apart from assignments and all the tests that happen so you know that there is a systematic way of way you know things happen okay so the teaching will be or style will be different but the content or you know uh the the teacher energy will be the same don't worry about it all right so here comes the next quiz on your screen get ready to join now and let's see if you guys are there okay let me just put it right up on your screen. Okay, I'm starting the next question on your screen.

Okay, I'm starting the question on your screen. Get ready. Make sure all your attention is towards V quiz. Okay, here it comes on your screen now. Alright, so what do we have over here?

When photoelectric effect if the intensity of light is doubled, then the maximum kinetic energy of the photoelectrons will become? Come on, think about it. Think about it.

If the in the photoelectric effect if the intensity of the light is doubled then the maximum kinetic energy of the photoelectrons will become how much? Hello Maha Lakshmi. Welcome.

Welcome. Participate in the quiz. Come on.

Double half four times no change. What is the answer? In the photoelectric effect if the intensity is doubled then the maximum kinetic energy of the electrons will become. Hi Isha. Welcome.

Okay. Will there be 11th class from the start for 10th graders after the boards in this channel? Please let me know. We will have the 11th standard classes, Tarun, but in a very different manner. Okay, let's see the final answer in 10 seconds.

Okay, come on, come on, come on. 9, 8, 7, 6, 5, 4, 3, 2, and there we go. We have it on your screen. A lot of you are saying no change, is it?

Yes guys there is no change. Reason if the intensity is doubled kinetic energy has no effect on it because when you change the intensity Then the number of photons will increase but the energy of a photon will never change. Each photon still has same energy just the number of photons will increase which will increase the current but the energy of a photon is still going to be the same.

Hence the kinetic energy will also be same. Just that there are more in number does not mean they will have more kinetic energy. It's just that more electrons will be ejected. That's all.

Let's have a look at the leaderboard coming up on your screen now before we go to the next question. Wow, Joel has gone to the top. Proud of you. Then Anbu, Raj, Anthony, Daljan, Janvi, Lok, Vishnu, Manogiana, Priyanka, Shrilata and Yoadeep.

Very good. Keep fighting guys. Things can keep changing.

Moving on to the next question on your screen now. Get ready. All right. So what do we have next? A photosensitive material would emit electrons if excited by photons beyond a threshold.

To overcome the threshold, one would decrease the... Interesting question. Come on, figure this out. To decrease, to overcome the threshold, one would decrease the...

What? Think carefully. What would you decrease?

Come on my warriors. Voltage applied, intensity of light. wavelength of light or frequency.

Quiz is not working Janhvi or you actually it should bacha. Just go to vquiz.in and just enter that code or just click on that link or was there a time limit for entering it? I don't think so there is a time limit you can join in at any point. Let me try it out on my phone bacha.

Okay let me just try it out. Okay, one second. I'm just trying to log in through my phone and see if it works. You need to log in, I think, through your Vedanto ID.

Even if you are not a member, you can still become a member by creating a free account. Even if you have a free account, it works, guys. I'm just trying to join in.

Meanwhile, I'll show you the results. Oh my god, one second, I'm entering the wrong password or email ID. I'll check it out later on. Show the leaderboard.

Okay, let's have a look. Guys, guys, guys, guys, guys, for the previous question, what was the previous question? It was all about you know, the threshold.

What if you decrease then what happens? All right, what rather what will you decrease? So Joel is again on the top, Anbu and Janhvi again on the top. See guys, the minimum energy. The minimum energy required to start the photoelectric effect is called as a work function and work function is hf0.

But if you increase frequency but if you increase the frequency then only you can then you only you can start the photoelectric effect. But the question said what you will decrease? Obviously you will not decrease frequency.

If you decrease frequency then the photoelectric effect will not happen. In fact you can write it as hc by lambda. When you decrease lambda then the frequency increases then the photoelectric effect can start because the work function has been overcome.

So decreasing the wavelength kick starts the photoelectric effect by increasing its energy lambda is in the denominator. Keep this in mind. So the question said what will you decrease?

What will you decrease? Frequency can't be decreased. It will be the wavelength which will be decreased.

All right. Moving on to another question coming up on your screen. Now, let's see what it is. The work function of a material is 5.3 electron volt.

The stopping potential for a radiation incident is 4.2 volt. What is the energy of a quantum of incident radiation? No problem, happens Isha.

Okay, let me meanwhile start to check if I can log in. Come on guys, I will do I can just I just saw it. I'm able to join in the week with guys.

And why the hell did this open up? Oops, why is this opening? Okay.

Yeah, I'm able to join the VQuiz guys. There is no problem. Just check it out once again. Okay, those of you are not just you need to probably log in through your account. Even if it's a free account, it is fine guys, even if it's a free account.

Alright, so that's the final answers. A lot of you answered B whether it is correct or wrong. Well, looks like you guys are correct.

All you need to do is just write it down in the photoelectric equation form. The energy of your photon, the energy of your photon is the work function plus E into vs the work function. is literally mentioned over here 5.3 electron volt and the stopping potential is also mentioned over here.

What is the stopping potential? It is 4.2. 4.2 plus 5.3 isn't it 9.5? Isn't it 9.5e? So that's the energy of the photon.

The energy of the quantum. Quantum means photon. What is energy of the photon? That's all they have asked. That's it.

You got it. That's it. Cool, shall we move ahead?

Alright, let's have a look at the leaderboard. Let's see who is at the top still. And literally guys, even if you are joining now, you can still participate in the WeQuiz right now. Just go to WeQuiz.in and enter this code. Wow, Joel is still maintaining his top lead.

Anbu and Anthony on 2nd and 3rd. Lok Vishnu, Janhvi, Priyanka, Daljeet, Yudip and Ankit Kumar Singh. Very good guys. I'll go to the next question after the next theory pointers.

Okay, let's go to the theory slides now. and see what's up in the theory slides. Okay, I think we'll have atomic structure. Yes, we do have atomic structure right away. So in this chapter of atomic structure or atoms, what you will have is the different theories by different scientists.

Each one suggested a different model of the atom. Each one had its own limitations and a good thing about that theory. But the model which is fair enough to describe most of the phenomena is the Bohr's model.

The first person to talk about you know the atomic structure and give a decent idea of how the atom looks like was by Thomson and then Rutherford and Chadwick then discovered neutrons and then we had the Bohr's model. So according to Thomson it was a watermelon. So imagine you know at those times in those days if you had just told that you know the atom is like a watermelon the seeds inside are basically the electrons and the red part is the positive charge and that's how an atom is everybody would have clapped hands for you everybody would hail you as a hero and your name would be over here instead of thompson that's what he said but okay not to discredit him understand even at even though the model looks very simple at those point of times you know to come up with that idea is very very difficult. Now why did he say that the seeds are like electrons and not the other way around is because they knew at that point of time is the electrons which move when you conduct electricity.

So that means electrons are freely movable, it is freely movable inside that conductor. So if it is freely movable it should be easily you know you can easily eject it so that's why he thought they are like small small tiny bits. which are spread out and you can easily knock them out.

That's what he thought and because an atom is electrically neutral equal amount of positive and negative charges are there so that's why atom is electrically neutral. But it failed many of the things it could not explain how spectral lines come or it could not even account for the scattering of the alpha particles when you pass it through a thin sheet of metal which was conducted by Rutherford. So then Rutherford conducted the most famous.

in a scattering experiment of alpha particles and when he passed the alpha particles through a metallic surface he found that most of the alpha particles were passing undeflected onto the other side he had placed a detector around it okay so he could detect where the alpha particles are striking most of them went without you know any deviation like you can see right over here some of them got deflected by a small amount That means when the alpha particles are positively charged, remember that. That means if they got deflected slightly, that means they encountered some kind of positive charge somewhere. So the alpha particles which are positively charged encountered small amount of positive charge, that's why they got deflected.

A very very few number got completely rebounded and they struck the photographic plate behind. That means... There are very few alpha particles which actually encounter that positive charge of that atom and that's when they get completely reflected back and this strike behind.

That gave him the idea that since all of them are passing undeflected so atom should be most likely empty only a small part where the positive charge is concentrated. So that's when he gave this model of an atom where there is a nucleus which is heavy positively charged and electrons are revolving around it because of the centripetal force by the electric force of attraction. But even this model could not explain so many things like the spectral lines and the calculations for ionization energy and so many other things. So then after his limitations came the, oh by the way you should know all these limitations for Bohr's, they can ask you for Bohr's.

Then came the Bohr's model of atom. So when Bohr gave the structure of atom, he gave it in a little bit more fancy and detailed manner and he said electrons Even though they are moving around the orbits, they still can retain their energy only in certain fixed energy levels or fixed orbits. These orbits are so special that even if a charged particle accelerates, it will not radiate energy. There is something called as Maxwell's radiation.

I don't want to confuse you too much. But it says that if you take a charged particle and accelerate it, then it will emit. radiation and it will die out and it will lose all the energy but electrons even though it is charged and even though it is accelerating it does not lose energy in those special orbits those are called as the fixed orbits and when an electron jumps from low to high it absorbs energy from a light particle which is photon and if electron jumps from higher energy to lower energy it emits photons that's what he said and those fixed orbits Those fixed orbits have angular momentum which is integral multiples of h by 2 pi. Very very important this law. It has integral multiples.

The angular momentum is in integral multiples of Planck's constant by 2 pi. Very very important. Okay.

I hope this is clear. I hope this is clear. Okay. Now remember these postulates. From Bode's point of view, this postulate is important from your competitive exam point of view and other things are fairly simple where nucleus is at the center, the electron revolves in orbits which are stationary and these are such orbits where energy is neither destroyed or created.

Only way you can transfer the energy is by absorbing a photon and shifting it to higher energy state or losing the energy in the form of a photon again. That's what it is. Now based on these postulates he was able to estimate the radius, energy, velocity, time period of an electron revolving around a nucleus and these are the formulas. You don't have to remember it like this. No, please don't remember it like this.

In fact, the only thing that you should remember is what it is proportional to. Radius is proportional to n square by z. The velocity is proportional to z by n. and energy is proportional to z square by n square that is something what you should remember okay and yes the constant values what is 0.529 0.529 is the radius of the first orbit of hydrogen atom for hydrogen z is 1 n is 1 for the first orbit so that is the radius of the first orbit of a hydrogen atom that's something what you should remember then you This is the velocity of the first orbit of again hydrogen.

If you put z is 1, n is 1, you will get that. And yes, there should be a minus sign over here because energies are always negative. The energies are always negative.

Keep this in mind. That's the total energy of the nth orbit. Keep this in mind.

All right. Now that you know this, now that you know this, yes, derivation is important for advance. Yes, Jain, it is definitely important.

Now for mains and need. it is not at all important. Okay, now if you look at the energy levels right over here, you will get a sense of how the energy levels are arranged.

Zero energy is for n is infinity, which makes sense. When you put infinity over here, it becomes so large that the energy becomes small, tending to zero, meaning you have freed the electron. Zero energy means it has no longer been attached or associated or bounded with the atom. Zero energy. Okay, so zero energy means it is no longer attached to the atom.

It has been freed. Anything which is less it is bound to the atom. So 0 is basically free and when it is negative it is basically bound. That's why sometimes it is also called as binding energy. You would have seen that in satellites, gravitation.

Keep this in mind. Alright, so you can see the spacing of lines is also not uniform because n square is there in the denominator. When n is 1, The energy is minus 13.6 electron volt and when it is 2 it is minus 3.4 volt and then as you go up and up the spacing reduces the gap is very less because there is hardly any difference when you jump from you know a very high state to a much higher state.

Okay why our energy is negative? See negative energy means it is relative to the highest energy which is when it is free. So imagine I tell you the energy is minus 13.6. Okay, electron volt. If it is minus, it is relative to this.

If you want to make this electron jump from here to here, you need to supply energy and the reference is assumed to be zero at infinity. Just like for gravitational electrostatics, you say that when the particles are infinitely apart, that's when their energy is zero. That's a reference energy. Like for MGH, you always take some reference, maybe the ground level.

So here the reference is infinity and that's where you have assumed it to be zero. So if you have to supply energy to reach zero, if you need to give energy to reach zero, that means your energy right now must be negative. I hope this is clear. Okay, understood. All right.

Let's talk about the last part in this which is called as your hydrogen spectrum. And you get amazing, you know lines. or spectral lines which come out of you know different elements which are like its signature you also have your own signature right you also have your own signature so even elements have their own unique signature which does not match with any other element that's called a spectral lines now why does it come is because when you agitate and when you give energy to the atoms they start You know, woggling, they start shaking, they hit each other, they transfer the energy and when they hit each other because of their temperature, they knock out electrons and these electrons can then shift to higher energy states. So, the temperature gives the thermal energy which can then knock out and which can supply energies to the electrons during the collisions. When the electrons go to higher energy states, they will not be happy for a long time.

They will want to come back. Like, why are you sending me up? I want to go down.

So they will eventually come down. When they come down, they are going from higher energy state to lower energy state. That's when you will see photons will be emitted.

That's when you will see light will be created. Depending on which orbit to which orbit they are jumping, their energy difference goes in creating that photon. So that's why each jump corresponds to a specific energy which also corresponds to a specific frequency of that photon. So that's why you will see some unique lines depending on their jumps from higher energy to lower energy. That's why you see this unique signature out here.

Is that clear my warriors? Is that understood my warriors? That's very important. And yes you have your Lyman, yes Ankit you have your Lyman Balmer Paschen series depending on the jumps.

If you jump from any energy state apart from 1 to n is equal to 1 that's Lyman. If you jump from higher energies to n is equal to 2 you have Balmer and then if you jump from higher energy to the lower energy which is 3 then you call it as Paschen series. So these jumps have been classified depending on where their final destination is final destination is one Lyman two Balmer three passion then bracket p fund that's how it is that's how it is clear okay now I'll just write down few equations the energy difference between you know the states or basically the orbits the orbits goes into the energy of that photon which has been created you So that will be hc by lambda. Now when you solve this further by substituting the formula of energy of you know the electron in different states.

You get this relationship 1 by lambda is R z square into 1 by n1 square minus 1 by n2 square. Very very important formula if you want to calculate the wavelength between two jumps. n1 and n2 are your initial and final destinations of the electron between the jumps.

R is called as Rydberg's constant, z is your atomic number. So that's how it is. Oh why is it named like this?

It's named based on who discovered it. That's all Ankit. Okay let's start with some quiz which is going to come up on your screen and here it comes. Let's start that quiz. Yep the question should be up on your screen in three, two, one, now get ready.

Okay so here we come with the next question is Bohr's model of atom. assumes Boards model of atom assumes which of the following the options will be visible on your screen in a bit train man sir if my home state NIT does not have home state OBC quota and I have filled the form in OBC so will I be allotted general category home state or national you'll be allotted general category home state train man not national obviously they will always give preference to your home state and then comes national is that okay train man The nucleus is of infinite mass and is at rest. Electron is a quantized orbit, will not radiate energy and mass of the electron remains constant all of the above conditions.

Guys this should not be infinite this should be finite okay this is not infinite just make it finite okay and is at rest okay and electrons is in a quantized even if you take it as infinite still it will be Okay, I'll tell you why in a bit because anyways the time is up. Okay, so guys the correct answer is all of the above. Yes, most of you are correct.

Strictly speaking, the nucleus has a finite mass but even if you make the assumption that is infinite mass it works because I'll tell you why. If the mass of the nucleus, if the mass of the nucleus is finite and if the electron goes around it, actually speaking even the nucleus should go around. nuclear should go around because their center of mass should stay at rest. Remember when two particles go around each other because of their mutual force of attraction, they always do so around their common center of mass. Now if you don't want the heavier particle to move like when the earth goes around the sun, we assume the sun is at rest but technically sun is not at rest, sun also wobbles around.

So, We make the assumption that the Sun is rest that means it is very very heavy it's very very heavy and that will make sure that the center of mass lies on the Sun. Same way the center of mass of the nucleus and electron is on the nucleus then the nucleus will not wobble it will stay there. So that can only happen if it is infinite but actually speaking it should be finite.

I hope this is fine. Next the electrons is in quantized form yes the energies are always fixed and only in those quantized energy states it will not radiate energy. Mass of the electron remains constant, yes it always remains constant, it never decreases or increases.

Perfect, let's see the leaderboard right now. Okay great, so we have Joel still on the top, Anthony still leading, Anbu Raj, very good Priyanka, sorry VLog, Kaushik, we have a new person, Janhvi, Manojnya and Dalijan. Wow, we have some new names coming up on the leaderboard.

Next question on your screen now. Here it comes. Here it comes.

The ratio of radar of the atom assuming Bohr's model A is, come on, let's see how many of you can get this. The ratio of the radar of the atom assuming Bohr's model A is, it's going to be an interesting one. Okay, here are your options. You can start working it out.

You have one minute to answer this question. I'll give you a hint. Think about the radius formula. Think about the radius formula, bachalok.

Okay, think, think, think. Okay, SSM, you study well, but I'm not getting, but I, well, I study well, but I don't, I am getting fear while studying how to overcome this. SSM, most likely it's the. fear which is coming out because you have not practiced enough pyqs so once you get a strong hold of pyqs that fear will go away so start with mock test start with some more good questions and Slowly start doing the PYQs without seeing the solutions or answer ki.

You will slowly overcome the fear bacha. Okay, let's have a look at the final answer in 10 seconds. Ankit, it should be showing.

I'm not sure why it is not showing. It should be. Mohan, watch this one shots. Also watch my regular classes.

It's there on YouTube also in the 12 standard pathfinder. It's there. The playlist series is there.

Watch the modern physics classes. It will take you 2 to 3 days max. Within 2 to 3 days, you will become an expert. Okay, just do that. Let's have a look at the results.

And looks like many of you are wrong. I'll tell you how to do this question. You need to see how many shells are there.

Remember, the radius, the radius is proportional to n square. Now if you look at this atom, don't look at the atomic mass number, look at the atomic number, which is 13. So 13 will be nothing but 2, 8 and 3. So there are basically 3 shells. Similarly, when you write for 52, 2, 8, 18, see how many shells will come. I think there will be 5 shells coming out over here. So when you take the ratio of the radii, R1 by R2, which will be N1 by N2, whole square it will be 3 by 5 whole square so 3 by 5 whole square is 9 by 25 that's the answer pyq can be asked in different ways in need bacha not directly they will not repeat but they can change the values or just they can change what is given can be asked and what was asked can be given they can change all these things all right so let's have a look at the leaderboard some of you are really maintaining your stand Very good Joel Anthony Anburaj.

Excellent day. And here comes the final question on your screen. Now, here it is. Very good Anthony.

That is very good. How 5 shells Ankit? Just write the atomic structure of it.

K, L, M, N. Ankit, you know right? 2, 8, 18. Check it out. How many shells will come? You will get 5 shells.

Yes, yes ZenBod, I will be doing one shots for 11th portions also but first preference for 12th term too because that is coming very soon. Okay, cool. So the ground state energy of hydrogen atom is this much.

When the electron is in the first excited state for helium then the excitation energy is. It's for helium, be careful. Is NCRT alone enough for modern physics?

Mohan? 90% yes, 10% maybe you might need some help, 10-15% from HC Varma. Because there could be some questions which require some good level of understanding and concepts and that I feel you will get it from HC Varma.

If you want to score 120 marks or 130 marks in physics then not needed. But if you are aiming for 120+, 140+, in physics then you need to study from HC Varma. Okay, Pathfinder is available for an entire timer. It is now called as 12 standard.

12 standard J neat. You will see it 12 standard J neat. You will see it physics, chemistry, maths, everything has been arranged. All right, let's have a look at the results.

The correct answer. Oh, very few people got it. I'll tell you what you have missed.

This is the energy of hydrogen. But what is asked is helium. They are completely different.

And it's excitation energy has been asked. So to excite it means you have to go make it go from one to two. So the energy difference that we are talking about here is E1 minus E2 modulus of that. So basically it will be 13.6 that's constant value. Z for helium, Z for helium is two.

So you will have Z square, which is two square by you know one square minus Z square. by 2 square this is what you're going to get just do the math 2 square is 4 and here you will get 1 so just do the math guys you're going to get the final answer z square by n square just do the math and you will get the answer yep so it should be it should be yeah it's not 3.5 it's helium it's not hydrogen be careful about it be careful okay just be little bit careful about it Alright, let's have a look at the final leaderboard. And let's see how many of you got it. NCRT alone.

enough for modern physics no mohan like i said for getting decent marks yes would you get top marks no okay so it should be working bacha if it is not working then i'll tell you what to do and yes we have our winner for today joel very good anthony very good yuvadeep very good congratulations bachalok you have done fabulous job out here you've got very good marks proud of you i'll just end the quiz right now so All you need to do is if you're watching the video right now and if you're still not able to join the telegram channel I'll tell you what you can do. One simple hack usually which works. So telegram channel just click on this. It is not working.

Okay you see this link over here in over here that t.me right just replace it with telegram just replace it with telegram and let put that enter button now you will be able to join it that's the only thing or change that you need to do that's it guys all right perfecto let's move to the last thing yep so guys if you enjoyed the session make sure you go ahead join the telegram channel so that you get all the important updates go ahead hit the like and subscribe button and yes all those interested in the crash courses go check out the link which is there in the description box Because crash courses are available for a very cheap rate of just 1800 rupees. Go ahead, check it out. All tests, assignments, lectures, recordings, everything is available just for you, both for GE and NEET.

All right. Thank you very much for tuning in. And I hope you guys had a great time. Bye bye. Take care.

And yeah, the crash course validity is till the last exam, even if it gets postponed. Don't worry about it. Bye bye.

That's it from my side. This was Shreyas here signing off.

Transcript for:Understanding Light's Dual Nature in Physics

Transcript for:
Understanding Light's Dual Nature in Physics