Hello guys, what's up? So today once again you can see my face with a, I mean in my hand you can see a blue chalk. Last time I remember it was yellow but this time I had got this blue chalk.
And so last time there was a different topic and now we are gonna do a different topic. You remember when I was teaching you in last class we were doing something related to dual nature, right? And I gave you this example of moms.
Like moms are always, sometimes they are very strict, sometimes they are very loving. Right? That means everyone is having a kind of dual characteristics. At one point of time you may be like relaxed, at another point of time you may feel like I am the most stressed out person. Right?
And similarly in continuing the discussion like that, last class we did discussing about the dual nature of matter. That means particles possess both the particle nature as well as the wave nature. Now having done with this, we need to move on to the second characteristic property which is something known as dual nature of waves.
So I don't know why whenever I write this word waves in my mind the only thing that comes is to draw something like this. Okay and waves you know they are shown they are known to show the wave nature. By the way what do we mean by wave nature?
Wave nature you will study the details in class 12th in physics, but wave nature means the light is known to show properties like diffraction. So, you will study about the topic diffraction light is known to show another property which is interference. Maybe the third property which the light can show something related to polarization.
So, all these are the characteristic properties which are in general shown by the wave and hence we say that these will describe the wave nature of any particular wave. Okay, but then that means it is a characteristic of a wave to show diffraction, to undergo interference or to undergo polarization. Right?
Now, the way I said the dual nature of particles. See, let me discuss this also side by side. I told you right when we were discussing the dual nature of matter, I said that matter was having mass and when the matter, the mass is moving with a very high velocity.
then it will possess the wave nature as well. Ok, so according to this particular concept you should be saying that ma'am if we have a football, let's say if we are having a football something like this, you are talking about the dual nature so what do you think that the football should also be looking like a wave but no right wave means you cannot determine its position at any particular point it is not easy to determine the position but for football if it is moving with a velocity v then you know right if the football is at this position or it is at this position or it is at this position you know everything right that means is it okay if I say football is also having dual nature yes guys see so for every particular object lambda is equal to h over MV Ok, so this is what is de Broglie equation that we have derived in the last class. Now listen to me carefully, if the particle is having a very very small mass, the particle should possess a very very small mass along with it the particle should possess high velocity which should be taken approximately as the speed of light. Clear?
That means I am saying if and only if the particle is very light mass and it is also moving with the speed of the light then only the wavelength that you will find out will be the characteristic wavelength and it will show the wave nature. But suppose you are talking about a football, the one which I have drawn here. This football is having a good mass m.
So, maybe the mass of football let's say maybe 200 grams or 300 grams. You do anything but you won't be able to provide a velocity of like the velocity equivalent to the speed of light to football. So, when you cannot provide the velocity as the speed of light, you can not provide.
That mean I will simply say that the velocity is less. So then also you can put the value of mass and the velocity in the formula, the same formula lambda is equal to h over mv. You put the value of mass, you put the value of velocity that is okay.
But finally when you get the wavelength, this wavelength will come out to be a number but this will be insignificant. Okay, like you know like if I simply talk about girls, I know like we girls have so many clothes, right? So many clothes means we have almost everything but we wear only a few of them and others are just like that, right? That means they are insignificant for us. of no use to us although we have lot more right.
Similarly when I'm saying that there is a football which is having a particular mass and is moving with a particular velocity that is okay. So it does have the particle nature plus it is also having the wave nature but the wave nature means the wavelength of this football is so damn insignificant that it accounts as if the football is just behaving like a particle. Okay, so if you want the football to behave like a wave then you need to reduce the mass of the football and you need to provide too high speed to the football so that it gets a significant value of wavelength. Fine? Now continuing with the same discussion, I was saying that when I'm talking about waves, the waves are said to follow wave nature because they will undergo diffraction, they will undergo interference process, they can show polarization, all these things.
But now the question might be ma'am, which particular phenomena is such that with the help of which you will understand that the waves are also having particle nature, right? So now in order to find out what is the second nature. So, this is wave nature and how will you determine the particle nature of wave?
This is what we will study now. And for this thing there is another topic which is known as photoelectric effect. So, let me just tell you what was done in the case of photoelectric effect. See guys what we finally did.
We tried to carry out an experiment by taking a metal. So, we have taken a metal plate and the metallic plate was maybe of potassium, rubidium, cesium. So, we have taken any particular metallic plate.
Okay, now what happened was we impinged it. light or let us say a radiation of a particular frequency nu. Okay? So, we have impinged the light of a particular frequency which is nu. Now, can you tell me what will be the energy associated with this light?
So, you will say ma'am Energy can be written as E is equal to H nu. So, the energy of impinging radiation is H nu. I have written it as 1. Okay, what you will observe is the metal.
I'm saying you are taking either rubidium cesium. That means we have taken kind of metals where the last electron is very loosely. held. That means maybe I have I am talking about alkali metals or something. So, I just want the last electron to be loosely held.
Now, what will happen see as soon as the light or the radiation of a particular frequency will strike the metal plate. So, this is a metal plate. So, as soon as the light of a particular frequency will strike the metal plate, you will see that the electrons are coming out and this electron is coming out which is moving also, so which is having some kinetic energy. Ok, now listen to me very carefully once again.
Don't you think last in my previous videos I would have given you this example that let's say this is a truck. So, let's say this is a truck, okay and in this truck, this is moving with very high velocity and the truck is very heavy, right? So, it must be having a mass, let us say capital M, okay?
And it's moving with a very high velocity, let's say V in the right direction. So, you can say somewhere here, fine? And now I'm saying a very small insect.
a fly or an insect is coming, you know right, the mass of the insect will be very very small, so which is small m and it may not be moving with that high speed, it is small v. Now when the two are coming close to each other and suppose they strike each other, so when this is having a mass capital M, velocity capital V, so it must be having a momentum. Similarly, when the insect is having the mass and velocity v, so there must be some momentum of the insect, momentum of the truck, right? And let me say when the two are colliding with each other, some some effect will be produced.
That means there will be either exchange of momentum, Then only you can say right that ma'am the speed of the truck will not get slowed down but the speed of the insect may die. Right? There may be some changes in the momentum. Similarly don't you think that when a radiation you know right radiation is maybe a wave. Radiation was a wave but now this electron which is present in the metal surface it is a particle.
Right? I am saying just imagine that there is something which is coming from outside and this radiation which is coming from outside, it struck the electron which is a particle and then I could see that the electron was getting ejected out. Guys, so don't you think there would have been exchange of momentum then only it is possible right that the particle is ejected out.
So, how can a wave eject out a particle? The wave could have ejected out the particle if and only if the wave would also be having a particle nature. Because momentum is what? Momentum is possessed by any particle with a mass m and velocity v. So, how can I say that a wave is ejecting out an electron? That means electron was a particle and if there is ejection of the particle that simply means that a particle is coming and striking this particle.
That means the wave is now having the particle nature as well. ok just as you the minimum amount of energy required to eject this electron is h nu not so minimum amount of energy required to Eject the electron is known as W naught and this W naught is also known as work function. By the way, how did we get to know that there is something like work function which does exist? So, what scientist did, listen to me very carefully. So, first of all scientists have taken this metallic plate.
Okay, and they knew that the electrons were loosely held in the metallic plate. So, they didn't randomly start with any of the incident radiation. They first have taken the radiation of lower energy. Like let us say first they took E1.
So, when they were taking E1, they found out that no electron was getting ejected. Fine? Then they took maybe of E2, then also they strike but then also nothing was getting ejected out. So, they continued E3, E4, nothing helped out but finally when they would have taken the radiation E5. So, it will take out the electron that means there has to be a minimum value which you need to supply then only this electron could be ejected out and the minimum value of energy that you will apply in order to eject the loosely bound electron this value is known as work function.
Fine? So, this is the value which is given by the name as work function. Now listen carefully, suppose I am giving an energy E6 and this time the energy E6 is greater than E5.
So when the energy E6 is found to be greater than the energy E5, then don't you think this will strike and now the electron will be emitted out and at this point of time the electron will also possess some kinetic energy. That means we can now write our final statement which is or which can be written as h nu minus h nu naught is equal to kinetic energy maximum. That means this is the maximum kinetic energy that can be possessed by the electron which is emitting out.
Where h nu is the energy of incident radiation. That is this is the energy which you actually impinged on the surface of the metal and this H2O is the work function. Guys listen very carefully this term work function is also known by the name as threshold energy.
So, what is threshold energy? Threshold energy is the minimum energy which is required, which has to be impinged onto the surface of metal so as to eject the electron. Okay, and this kinetic energy is nothing but the maximum energy that can be possessed by the electron in the form of its velocity which is written as V. Okay, now because these electrons which are emitting out they are nothing but they are emitted out only and only because of the reason that they are coming out in the terms of photons right.
So, these are known as photo electrons. So, why photoelectrons? Because until and unless you have impinged a particular radiation, these electrons would not have come out. So, they are coming out just because of this particular photon that you are impinging and hence they are known as photo electrons. Okay, so guys note it down so that we can further continue with the detailed discussion.
So, this part is important and you need to note down all the things so that we can continue with the detailed discussion. Now, the question says that the Rutherford's experiment which was, which established the nuclear model of the atom used a beam of what? That means he simply asking us to do the details of Rutherford's experiment. So, the Rutherford experiment that was done in order to establish the nuclear model of an atom. Like Rutherford was the person who said that there is a nucleus in the atom, right?
So, this used a beam of what? So, let us first gather the knowledge about Rutherford's model of an atom once again. See guys if I'm not wrong we have discussed right that in the Rutherford's model of an atom first of all we have taken a lead chamber.
Now in the lead chamber you kept a radioactive atom which was radium and after that we have also taken a very very thin sheet which was made up of gold. Right? So, we used to call it as gold foil.
Now, you remember right that radium was getting disintegrated and it led to the release of positively charged particles. I remember telling you in details that those positively charged particles were helium, nuclei. They were not helium atoms. Why they were helium nuclei? Let's see.
So, we know right helium is atomic number 2,4 so there are two protons, two electrons and there were two neutrons. Right? Protons I'm showing with positive electrons as negative, neutrons as neutral.
Now with the release of two electrons we will be left with two positive and two neutral particles. Right? So this was our Helium 2+. So, I remember telling you that the helium 2 plus cation were released and these helium 2 plus cations are nothing but see it is protons plus neutrons which is the helium nucleus. So, a beam of alpha particles or in other words you can call them a beam of helium nuclei were released.
Let us read out all the options one by one to figure out if there is any correct answer and if it is which one is the correct answer. Option number A says beta particles. No guys, never ever we said beta particles.
Gamma rays, no. Then the third option says helium atoms. No, helium atom is He but I know that alpha particle is positively charged so not even this and the fourth one is helium nuclei.
which impinged on a metal foil and got scattered and that is the perfect answer for question number first and hence of question number one can be written with the correct option as option number B okay having done with this particular question now let us move on to the second question just give me a second so as to prepare the board Ok, by that time I can switch on the second question for you. Read out the second question which says that many elements have non-integral atomic masses because, so first of all he is giving us a fact that so many elements in nature they are having non-integral atomic masses. Ok, and then he has given us the answer why or which of them. Fine?
Let us first of all try to concentrate about chlorine atom. You remember guys chlorine atom is having 17 protons and I remember while I was discussing the isotope thing with you, we said that chlorine 35 was one isotope of chlorine and chlorine 1737 was another isotope of chlorine. By the way what is this 35 and 37?
This 35 and 37 stands for mass number or atomic masses right? The number of protons plus neutrons which are present in an atom. Now see guys since mass number represents the number of protons plus number of neutrons. So, whatever may be the number of proton, whatever may be the number of neutron but the total number of proton plus neutron will be an integral value. Am I right?
Now, the main problem is that since Cl35 let us say might be present in 75% and this might be present 25%. Suppose for example, I have a bucket which is having 100 atoms of chlorine and then in that bucket the 75 atoms of chlorine will be Cl1735 and the next 25 elements of chlorine will be Cl1737. Right?
You remember how we calculated the average atomic mass? So, I have written the formula. The average atomic mass was written as the like 35 the mass number into 75 atoms are there.
So, let us say 75 divided by 100 plus then the other one is 37 into 25 by 100. Ok, and suppose if you solve it you'll get the answer as 35.5. So, in general we can say that the atomic mass of chlorine which you will be using in questions will be 35.5. But is it correct to say that this is coming because of the number of protons plus neutrons? No right?
So, this non integral The non-integral mass of any particular element is found out. Why? Because the element is there in the isotopic form. Not only this, I'm also very sure because the two isotopes occur in different different amount and since they are occurring in different different amount, the atomic mass may be found to be a non-integral value. Right?
Let us look at the options. So, reading the question once again, many elements non-integral masses because they have isotopes. Yes, that is correct.
Because the isotopes have non-integral masses, this is wrong. See, I have specified this thing that the two isotopes were having atomic mass of 35 and 37. So, these were integral values because even if you are talking about isotopes, they must be having some number of protons, some number of neutrons. You sum them together and then only you will get some integral value because proton will be an integral number. There can be two protons, three protons, twenty protons but there won't be ever 20.1 proton, right?
So the number of protons plus neutrons together will be coming out to be an integral value. So this B option is wrong. Moving on to the third option, the isotopes have different masses, that is correct. So, we can simply say that the isotopes are having different masses, this is also correct.
The next is the constituents neutrons, protons and electrons combine to give fractional mass. No guys, I'm not even taking into account the masses of protons, neutrons and electrons. I'm just taking into account the numbers of protons and neutrons which are present in any atom so as to call it as atomic masses.
Fine? The question was really interesting because he like many students can get confused in option number D right many students can get confused in option number B as well but the correct answer for this particular question is A and C ok so guys this was about the second question now it's a time that we can move on to the third question Just give me a second once again. Ok, so we have another question which is question number three. You can read out the question which is there on the screen and the question says that Rutherford scattering experiment is related to the size of what? So, he's talking about the Rutherford's model of an atom and when the experiment was done the size which the size of which thing was found.
See, now I'll tell you how students get confused. You know students like you, you would have marked up a formula. So, there is a formula like R is equal to n square h square by uh So, you will be doing like 2r is equal to 2n square h square by 8pi square m kz e square. In other words, I have seen students writing this formula as r is equal to n square h square by 4pi square m kz e square. So, these people have marked up the formula.
And then they will be thinking ma'am the formula was given by Bohr. So, they would have marked Bohr. So, this is what? This is the formula of radius of nth orbit of an atom right, so they'll simply say ma'am this was done for an atom.
No guys, no. This formula has got no link with this particular question that has been written on board. The question simply is talking about the Rutherford's alpha scattering experiment and while Rutherford's alpha scattering experiment was done, these kinds of formulas were not taken into consideration.
What was done in the Rutherford's model of an atom? See, we have already done it, no? Right now also I explained you people were to take a lead chamber keeping a radioactive particle here which was undergoing disintegration to form alpha particles. Alpha particles were supposed to be positively charged then they were allowed to pass through a thin gold foil right and finally you could see that most of the, so what were the postulates? Let's directly come on to the postulates.
So the postulates were that most of the alpha particles were moving in the straight line without any deviation. That means too much space in the atom must be empty. But too much space is empty has got no correlation with the size of an atom, no.
The second observation was that when the alpha particles are coming they come and then they get deflected towards large with the larger angles. Alpha particles were coming they were getting deflected at larger angles. Now why the alpha particles were getting scattered at larger angles then also we were we were saying This is because the nucleus must be positively charged and since nucleus must be positively charged, the alpha particle which is coming is also having a positive charge.
So, when positive and positive will interact then we can say that they will repel each other and hence they will be moving, so they will be deflecting at larger angles. Okay, but we also had a third observation in our mind and the third observation said that when the alpha particles were moving in the straight line only a few alpha particles were such that they were coming back by an angle of 180 degree okay so all the alpha particles were coming back at an angle like very very very very few alpha particles were coming back at an angle of one degree and when the alpha particles came at an angle of 180 degree like only one out of 20,000 atoms alpha particles were coming back that means the space occupied by the nucleus is really very small because if the space occupied by nucleus would have been big enough then many of them