this is chemistry 2 unit number four and episode number one we start our lecture about structure of atoms atoms are very small and to have any idea about internal structure of such small object as atoms we need tools also which also will be very small and it can be electromagnetic wave so electromagnetic waves help us to figure out what is inside atom okay let us start with some terms first wave what is wave wave is vibrating disturbance by which energy strand transmitted wave has several characteristics these characteristics are wavelengths frequency and amplitude we are actually interested only in wavelengths and frequency in in this unit wavelength is distance between identical points on successive waves Okay so if I have distance from one Peak like I say two second Peak to identical points I have wave legs actually this wavelength is one wave one Wave It's one wavelength wavelengths is measured in meters and we use letter Lambda for it frequency is number of waves that pass through the particle point in a second so I just need to measure how many waves um will be in one second so if in one second I have this much waves this means I have high frequency if in one second I have just this much waves it will be low frequency frequency is measured in hertz or one course is the same as 1 divided by second or second in power negative one we also have characteristic which is amplitude which is vertical distance from the need line to the peak but we are not interested in this characteristic okay in this unit we are interested in electromagnetic wave because electromagnetic wave is something that help us to investigate inner structure of atom electromagnetic wave consists of electric and magnetic fields and these two components of electromagnetic wave have the same wavelengths the same frequency and the same speed but they travel in mutually perpendicular perpendicular planes I have a nice simulation here and by the way if you click I believe I don't know where um if you click some on online Link will be in in in your um Word document you can see this simulation so look at this I can see plane of electric field and I can see so this is plain Green Arrow shows me electric field component of electromagnetic wave or I can separately see plane of magnetic field component of electromagnetic wave and this green arrow shows me magnetic field component but my weight of course exists like this like green and red components and here is how my wave electromagnetic wave travels electromagnetic radiation is my our next term electromagnetic radiation is emission and transmission of energy in form of electromagnetic wave electromagnetic radiation can be gamma radiation or x-ray or ultraviolet visible light infrared radiation microwave radio wave all these are nothing else but electromagnetic radiation and what is important to understand that radiation behind radios visible light nuclear blast is exactly the same thing it's just different amount of energy um you can think about this like diluted solution or concentrated solution but actually it's the same substance okay so um what is different about gamma radiation and radio origination they have different energy can you see that gamma has higher energy and radio waves have low energy and everything that is in between will have medium energy all electromagnetic radiation or electromagnetic waves um have the same speed and we call it speed of light speed of light is three multiplied by 10 in Power 8 meters per second this will be speed of light in vacuum and in another medium it might be slightly different but it's okay for our purposes to um assume that speed of light is just three multiplied by 10 and Power 8 and that is it so actually gamma radiation visible light radio waves all these waves they have different energy but they travel with the same speed with speed three multiply by ten in Power 8 meters per second here we have our first important formula which connect together wavelength and frequency of electromagnetic light and a product of wavelengths and frequency is of Light which is three multiplied by 10 in Power 8 meters per second yeah before I press it to example number one I want to show you uh this table we visible light is special for us people because we have tools eyes which can see visible light but from the point of view of physics it's just normal radiation normal electromagnetic waves here are colors and wavelengths which are responsible for these colors for example Violet it's approximately 380 for 30 nanometers by the way one meter it's the same as 10 in power 9 nanometers nanometers very very small meter is something like this um yeah and some other numbers are given in this table I want to point that in different resources in different textbooks these numbers might be slightly different but it's okay it just because those numbers approximation approximate ranges of colors let us proceed to example number one they ask us to fill the table we know that speed of light and it will be constant is three multiplied by 10 in Power 8 multiplied by 10 in Power 8 meters per second and in first in first example they gave us a frequency new new is given 6 multiplied by 6 4 multiply by 10 in power 14 Hertz and wavelength is wanted and formula is C equals Lambda multiplied by Nu if I want to know Lambda Lambda will be speed of light C divided by Nu and I just plug numbers Okay so here is my formula and I plug numbers here three zero zero multiplied by ten in Power 8 meters per second divide by 6 4 multiplied by 10 in power 14. okay I have shirts but hers is nothing else but one divide by second y divided by second okay I plug numbers in calculator and you for sure will might have questions like this on exam what I asked you to do when you plug numbers in calculator please hug your denominator put numbers in denominator you in parenthesis okay so I have three multiply by 10 in Power 8 divided by parenthesis C 0.4 multiplied by 10 in power 14 uh my number is um I I give you number in scientific notation for 69 multiplied by 10 in power negative one two three four five six seven negative seven and it will be meters how do I know look at this my units are meters per second divide by one second it will be meters per second multiply second divide by 1 seconds are canceled so I have meters let us convert this to nanometers Because by the way can you see that my visible light here is given in nanometers because we do this just time I show you in details so to before 69 multiply by 10 in power negative 7 meters and I know that one meter is the same as 10 in power 9 nanometers in setup like this my meters will be canceled so I need to multiply these two numbers and I'll have four 69 Nana meters okay what color of light is this if we look at our table for a 69 I see that for 469 it will be in this region between 430 and 480 so it will be blue light okay let us move to the next problem speed of line light again it's constant so it will be three multiplied by ten in Power 8 meters per second here is Lambda is given which is our um speed of light and it's given in nanometers but when I want to calculate um frequency I need um my I need to convert nanometers to me so um let us do right now if I have 5 21 Nano meters I know that um 10. in power 9 nanometers it's the same as one meter you see that now I need divide this number by 10 in power 9 and this will be 5.1 I give my uncertain scientific notation multiply by 10 in power negative seven meters okay and uh in this case new is wanted again I start with this equation now I want this guy I want my frequency in my frequency when I um will be C divided by Lambda I when I rearrange my formula okay and I plug numbers three zero two zeros multiply by ten in Power 8 meters per second divide by and again something that in my denominator should be in parenthesis I have five 21 multiplied by 10 in power negative 7. meters K3 multiply by 10 and power eight divide 521 multiplied by 10 in power negative seven okay uh my answer with three significant figures will be five uh seventy 6 70 76 multiplied by 10 in power 14 and it will be second in power negative 1. or you can write it that you have 5 76 multiplied by 10 in power 14 Hertz because second in power negative 1 is nothing else but yours okay and also they ask us about color of light color of light can be easily deduced if I know by nanometers in this case it's 521 521 521 is between 480 and 560 so it will be green light let us talk a little bit about our results I see that in this case in in case of in this case um in case of green light I have bigger Lambda I have bigger Lambda and uh smaller frequency and if I compare it with blue light and blue light has smaller Lambda because can you see that four C 9 is smaller numbers than 5 21. but frequency will be higher okay let us move let us just keep this information in mind right now and uh let us move next term we need to understand is quantum kabantum actually itself it's discrete quantity of something of anything and example which I think is good example here is money U.S money consists of coins and bills so we can say that any coin or any bill is Quantum of money so I can um give you some amount of money using uh using 25 cents quarters or using pennies but I cannot give you half of the coin if I want to give I can I keep I can give you some amounts of money using discrete unit like for example if I want to give you money using 200 bills I cannot just um break my 200 bills to two parts just cut it and give you half of it because this is like discrete Quantum of money the same if I want to give you one dollar using this Quantum this discrete coin coin I can give it to you but I cannot using this Quantum give you let us say 48 cents it's impossible using this Quantum no so quantum like um definition of it it's discrete quantity so okay any one coin or bill is quantum of money so if we have one to quanta of something we can say that money is quantized and this means that money consists of quanta and money can be given or received in integral multiples of coins of bills it probably the easiest way to explain this once more time I give you one more example with penis penis is smallest possible Quantum of money for sure I can give you like two cents of 48 cents using using pennies but I cannot give you zero five cents so this is impossible because because it's impossible we don't have smaller than one cent if we convert this term to more scientific subject as physics we can talk about energy you don't vote classical physics thought that energy is continuous like ramp so physicists thought that energy can be given or received in any amount on any mode but actually in Quantum word properties can give properties can have just some particular values like Steps in staircase so in quantum physics we we will see it that energy is not continuous it is like staircase so energy can be let us say five Jewels for example or seven joules it's kind of fixed value so let us read these information to conclude what was said the difference between classical and Quantum approach in physics is illustrated by difference between RAM and staircase on RAM every spot along the way is available in the quantum World some properties can only have particular values as though they were restricted to the step of aesthetic of staircase so for example you can stand on step number two three or four but you cannot skip stand on step 267 or 4 28. and um scientists call each of these discrete steps one two from Latin word of how how much I want you to understand some idea when why I described about coins and bills not vanta are identicals identical so you see that Quran quanta of money can be like one coin who were five one cent or five cents or even two hundred dollars or one dollar um but so quanta can be big or small but but still they are like certain packages certain discrete numbers which are allowed okay let us move to the next piece of information yeah here is more scientific term for quantum vantum is discrete quantity in this case of energy not money that can be emitted or absorbed from the electromagnetic radiation okay so now as we know what kavan Quantum is let us proceed to the first piece of information which lead us to better understanding of atom and this piece of information is the energy is quantized and energy is franchised means that energy can be received or emitted in certain packages um who and how discover this it was max length and he explained black body radiation Spectra okay I need to explain this experiment and I will try to be to explain it as easy as possible because we absolutely do not need to know this in depth what does it mean what is it black body um actually any solid solid object can be thought eat e s black body but let us say we have cube of metal iron let us say and this will be black body why is black body if I take my cube of metal and I have no light when it night I will not see it so for me it will be absolutely black now imagine that I will take my iron my my metal cube of metal litter seats iron let us be more specific it doesn't matter actually which one which metal and I start to heat it if I heat it to approximately 1 000 Kelvins um in one thousand killings it's if I remember correctly it's about 1013 Fahrenheit so for sure it's very high temperature if I hit my cube of metal to this temperature I will see that even at night with no other light you is possible my metal will will be red hot red if I increase temperature to 200 Kelvins my piece of iron change color it will it it will still start is still to start to grow with yellow light if I even increase temperature more my light will be my light which will be emitted which I see from this piece of cube will be yellow white then um like white and if temperature even hotter it yeah I will see that this is blue this is something these colors these colors is something that can be absorbed I can see it but you know scientists don't want only see colors they want to measure something so okay we see observation is hard objects emit light and a color of light depends on temperature of object if I if I take let us say no piece of iron but I have star like stars on the sky and I hid them still the color which I see depends only on temperature scientists wanted to measure I told you this something so scientist measured intensity of Light which was emitted by heart object versus wavelengths and when they measure this they obtained curves like it's shown here so for example a this curve this is experimental data obtained for 6 000 Kelvins this curve 10 for 500 kelvins and sodium everything is good but what was um strange when scientists tried to calculate this curve using classical physics their prediction was different that experiment so technically experiment and theoretical calculation where in in Conflict so can you see that for 600 Kelvins here is experimental data and here is prediction so they are they are not in agreement in science when something is not in agreement with experiment if theory is not in agreement with experiment this means that theory is bad and we need to change it that theory that was used for prediction for classical prediction was energy is continuous energy can be given or um immediate in any values any values are possible and it was lamb who proposed something revolutionary new he proposed that energy can be gained or lost only in whole numbers of intervals H Nu in Quantum in quanta and what does it mean this means that energy is quantized quantized means it it can have just certain values this means that atoms and molecules can possess only certain discrete energy values and values in between in between in between not permitted by the way first scientists that scientists thought that this staircase quantized idea was kind of glitch but actually it was not yeah and I also if you click on um on on this link you will see something and I will show you it right now so this one is simulation so look at this e if I have temperature 5 uh 50 kelvins it's pretty low temperature then my here should be object my object my salad looks really like black if I increase temperature to let us say one thousand 50 gallons can you see that my object start glowing as red when I even increase more temperature for example for 200 2030 kelvins I see my object as Orange and increasing temperature gives me a like yellowish something and as I increase temperature for 30 it's even um more like white um and so don't look at this I increase temperature now it's five thousand 350 and you see it's like white and if I increase my very hot object will be blue so here is simulation which shows us this experiment okay so blank set the energy is quantized and this means that energy can have just discrete values and he said that energy can be gained or lost in whole intervals H Nu what is h here H is known now as land constant and plan constant is 663 multiplied by 10 power negative 34 joules per second the joules multiply by second it's very small value and um new here each new new is frequency and um also we can rearrange this formula here we have plan constant speed of light and Lambda which is wavelengths okay second piece of information so far so far we know that energy is paradized a second piece of information that light is not only electromagnetic wave but it is also particle and now we know we use special word for this photon um so you see this pretty picture so light not only wave which was thought In classical physics but it also particles photons and it was Albert and Stein and how did he come to uh this conclusion he explained photoelectric effect vote for the electric effort is if you have sheet of metal and you shine some light on this metal on some conditions electrons will be ejected from the surface of this metal and when electrons ejected flow of electrons is nothing else but current and using uh emitter we can we can measure this current but actually what was strange in this photoelectric effort that light which Shine On piece of metal must have certain minimum frequency and it's it's called threshold frequency and urine flow indicates how many electrons per second are released let us keep this for now and second piece of information energy of Photon of Light which which is shine on our piece of metal is less that energy required to remove the an electron that then electron will not be ejected regardless the intensity of radiation and if Photon has enough energy the Collision result are immediate ejection and um ejected electrons were with where high speed electrons okay to understand this explanation better let us actually run mental experiment and we um not only it will it not only be mental experiment we also have some simulation okay so let us say we have some metal and we have red light red light is light of low frequency low frequency and I will tell you more it is it it it is low energy actually low energy means low frequency the wave theory or classical Theory that if I shine some light on some metal and no electrons ejected then what I need to do I need to increase intensity of light or increase brightness of light so uh they saw that if they um shine Red Line no electrons were ejected so using this logic they increased intensity of red light still no electrons and it was strange because classical classical physics predicted that electrons should be should be should be um ejected should break free when it absorbed enough energy from light of any color so let me show you this nice demonstration so you see I have read light so what what you see here are four times of Light which shine here here is sodium metal but no electrons no electrons and even if I absorb density of my eye yeah if I absorb if I increase I increase intensity of light see I still so you see that more red light shining I still have no electrons this was classical physics couldn't explain this okay then they used green light and you know what what happened green light um caused some electrons ejected from the surface of our metal there according wave theory they saw that if they increase intensity of green light they should have electrons with higher speed so this was expectation of classical physics but instead of this when they're in increased intensity brightness of blue off of green light they had no higher speed electrons but just more electrons okay let us see this so okay instead of red light I now have green light okay can you see that some electrons are ejected and you see that my M meter show shows me some current I increase brightness so I increase intensity um the speed of electrons is the same but I just have more of them more more electrons how do I know that I have more electrons because I have higher um value for current and current is number of electrons per second okay even higher intensity I have even more electrons okay and now let us return so but is it possible to observe electrons which really have high speed yes if I have light of higher frequency like blue light I can receive I can receive electrons which are ejected with higher speed look at this so now I am with green light and when I have blue light you see that electrons which are ejected have higher speed why it's so it is because one photon with energy H knew kicks out one electron with matching energy so photon light possesses particle-like properties so we see red light each new photons where very low energy so they cannot kick out electrons and number of number of weak red photons couldn't help but when I had photons of green light which are matching energy with electrons yes they could kick out electrons from the surface of metal if I have more importance of matching energy more electrons were eject and only if I had photons of very high energy that they not only kick out electrons from the surface of metal they kick out them with high kinetic speed with Sky kinetic energy which gave them high speed Okay so because of this experiment that one photon kick out one electron of matching energy we can say that yes Photon possesses per particle light particle like um properties so it was a Einstein who suggested that beam of light is really a steam of particles and these particles of light now called Photon each Photon possesses energy H Nu so light both have wave nature and particle nature this is supposed to Revolution for now now for us it's like okay but for scientists of those days it was Revolution okay next information is that energy of a electron is quantized so you see we um approach to our atom because our electrons is something that is inside Adam energy of electron quantized and it was Nils War who um came to this conclusion and how he came to this conclusion he explained the emission spectrum of hydrogen okay what emission spectrum is emission spectrum is electromagnetic radiation emitted by source and um emission spectrum looks somehow like this by the way if you click on this um link you will see it they looks like this so you see some line and this line represents wavelengths and also some pretty colorful other lights so for hydrogen emission Spectra Spectrum looks like that four lines um like violet like blue light blue or green and um red here by the way if you click on hilum hilum has its own emission spectrum here is the spectrum of lithium sodium Mercury and neon actually emission Spectra was known for a long time and they were used like fingerprint of some element so if I had a spectrum like this I can I can check with reference book and say okay this is neon because it has this light lines and hydrogen has this line so if any if I receive any unknown spectrum and it looks like this I know immediately that my sample for which I measured this spectrum was hydrogen okay so yeah every element has a unique emission spectrum bore needs more postulated that electron is allowed to occupy only certain orbits orbit it was his term term Elton is allowed to occupy all the sorts in orbits of specific Energies in other words the energy of electrons are quantized so look at this we have nucleus this blue is nucleus and we have all beat number one orbit number two I I didn't draw other orbits it's not too illustrate idea and electron can be on orbit number one or orbit number two but it is not allowed to be in between so it's allowed occupy only 13 orbits of specific energy um how he explained this so a simple uh here is explanation of um emission spectrum simple of hydrogen gas is placed into a in a tube containing of two electrodes so actually you see that a sample of hydrogen is um placed in in in test in some tube and here some electrodes when electricity is applied to simple atoms of hydrogen gets excited get excited because too much energy is plugged to the system during the excitement events electrons absorb some energy and jump to any higher level to any higher orbit and the more energy is absorbed the higher the job so look at this if we have our initial electrons of hydrogen on first orbital oh I'm sorry on first orbit it's not orbital yet it's orbit but some energy is blocked it can jump here or if I give more energy here or if kick was pretty strong it can jump here or here or here which is actually shown in this second second diagram my green initial electron can jump on any level deciding how strong the kick of energy was then excited state is not stable state and excited electron fell down pretty quickly at any lower energy level any lower orbit and during the falling event electrons emit energy so you see I was here but then I come back I can come back from um three two two or from three to one so actually it's shown on this picture so you see if I have excited electron here it could return to level number two or it can return to level number um level number two or level number three on any level on any level or level number one and what is important when energy is emitted some of this energy visible energy so uh can you see that when I have excited electrons at level number what is it level number six and when it returns to level number two and energy emitted I will see in my Spectrum this purple light uh when electron excited electron from level five returns to level two it emits light which corresponds to this blue light which I see on hydrogen hydrogen emission spectrum when a electron excited electron from Level number four returns to level number two it emits some energy which corresponds to this green light and when electron from Level number three returns to level number two ah it emits some light which corresponds to this red a red line on my emission spectrum I also have other transition for example it can go from highest level to level number one or any other Transitions and their corresponds also to some light to some to some light but you see that this is you we like ultraviolet light or it's in infrared light I cannot see it with my eye for sure I scientists can measure it using special special machines but these four lies four line and four lights is something that I really absorb in this emission spectrum so can you see so can you see that uh transitions from certain energy levels corresponds to some lies so um let us read some information yeah the color of a emitting light corresponds to one of the lines of the hydrogen Spectrum some electron transition produce lines in ultraviolet or infrared parts of spectrum and we cannot see them by Naked Eyes so these fixed orbits of certain energy can be explained um can be explained by um so emission emission Spectra can be explained by this fixed orbits okay I and also I want to explain um how this emission Spectra produced so here is nice picture this is by the way how a sample of hydrogen looks like so it looks mostly like red lime but can you see that I have to which have hydrogen gas with some electrodes I have lens uh and I also have prison light which produced by hydrogen gas in This breeze divided by 13 13 lines and these lines lights lines of light are visible in in here in my Spectrum okay let us move to the next piece of information so War showed that the energies that the electron in hydrogen atom can occupy are and here's empirical formula empirical formula means formula found by um bound experimentally this formula we have RH with which is River constant and we have 1 divided by n in power two and um have num can have numbers one two or three and this is principle quantum number we are going to talk about this in next episode but you see that this number should be simple whole number Okay so we have one more formula which was derived by [Music] um Bohr and um during the emission the electron drops to lower energy state so like shown this picture so during the emission for example from six two two from six to uh from Level number six to level number two but actually we can calculate energy which is emitted when this event happened and this formula Delta H this is change of energy between two levels is H Nu H is constant Nu is frequency of Light which is emitted or it is read back constant and we have one divided by level initial in power 2 minus 1 divided by level Final in power 2. let us solve some problem calculate the wavelengths so wave length is wanted of the radiation emitted by a hydrogen atom when electron makes transition between level three to level two so what happened we have our nucleus one two three and our excited electron um yeah so uh final stick our electron was here initial so it was it was here so this is nucleus electron was here and we gave our electron some energy and each jumps here to level number three so this level number two is number three okay first I will calculate Delta e my Delta e is r h River constant one and two initial minus one n in power two final let us plug numbers third constant is 2 18 multiplied by 10 in power negative 18 joules and multiply by 1 divided by n initial one or one divided by 2 in power 2 because you see my initial is 2. minus 1 divided by my final is three three in power 2. so it will be 218 multiplied by power negative at 18 multiply parenthesis I just plugged everything in one one divided by two in power 2 will be 4. and minus 1 divide by 3 in power 2 will be 9 okay I have this number it is three zero two I round okay multiply by ten in power nineteen and it will be joules actually my calculator answer is three zero two seven in Period multiplied by 10 powered negative 19. okay uh but can you see that actually what is wanted Lambda is wanted we also have um equation which was given a little bit earlier should be somewhere here yeah that our energy is H U or H C Lambda so I can rearrange this formula and find Lambda if I know energy okay so my e is H Nu or it's c h multiplied by C and divide by Lambda I want Lambda so I rearrange it I don't describe my Lambda is H multiplied by C divided by E and I plug numbers uh Planck constant 6 63 multiplied by 10 in power negative 30 core joules per second let me check it this is correct okay six six sixty three ten negative 34. 3 yes speed of light is constant three zero zero multiplied by ten in Power 8 meters per second and energy we just calculated it three zero Twenty Eight I'm going to use my calculator answer not something that I rounded here I'm not rounding in the middle of my calculations okay I will have 53 multiply by 10 in power negative 34 multiply by 3 multiply by 10 in Power 8 and divide parenthesis I do copy paste and I see that I will show I will show you uh answer in scientific notation okay six fifty Seven multiply by 10 and power negative 1 2 3 4 5 6 7 negative seven meters but I one meter is the same as 10 in power 9 nanometers and I want to convert it to nanometer so I have six 57 Nano meters here's my answer so calculate wavelengths my flave wavelengths is this much nanometers and they ask me identify the spectral line produced by this Transit transition okay 675 675 um 675 actually 657 57 I see this on my calculator 657 corresponds to red light red light because yeah would E7 so I have 57 yeah so this is red light so this transition will correspond to red light okay so so far we know energy is quantized energy can have certain values numbers we know that light not only wave but also particles also know that energy of electrons are quantized and what does it mean this means that electron can have just can occupy certain orbitals sorting orbit sorting orbit 13 levels of certain energy certain orbits now let's press let us proceed to the next piece of information electron is not only particle electron also wave electron possesses wave-like properties and guy who came to this conclusion was Louis de Brule he was french guy and uh how he came to this conclusion he said that electron is standing wave okay probably first of all I want once more time to show you something so let us start with war war so you see that this blue is kind of electron and it can uh be on certain orbit orbit so this is orbit number one now let's look at this if I move to higher or orbit it can orbit number two orbit number three n equals three orbit number four bit number five so it's possible to jump to any orbits orbit number six orbit number seven and actually so far but it's impossible for electron to be in between and um now let us move to the bro okay so I said that de bro said that electron behaves like standing wave now what standing wave is extending wave is wave which appeared to be vibrating vertically without dreveling horizontally I will show you simulation which explains what what wave standing wave is so can you see that um we have Green Wave and Blue Wave on this picture and green and wave Way Green and wave they are moving uh actually I see that Blue Wave moves um from right to left and green from left to right so they move with opposite direction and both of them produce other wave red one and red one is known as standing wave and standing with wave which appear to be vibrating vertically without traveling horizontally so can you see that this Red Wave Red Wave which is standing goes like up and down up and down but it doesn't move horizontally you can absorb standing wave when you pluck guitar this something that you see it will be standing wave uh so de bro proposed that electron is nothing else but standing wave why is electron in bore atom restricted to obtaining their the orbital nucleus at certain fixes distances so why electron can be here here but only in between but why is restricted to to to have certain orbit because according to the brawl electron bound to the nucleus bound to the nucleus behaves like standing wave and um one standing wave seeds the first orbit like it's shown here one standing wave feeds one orbit first two standing waves fifth second orbit three standing waves one two three one two hits third orbit and so do on um I will show you this on this nice simulation Deborah look at this when I have first uh first orbit I have here just one standard wave maybe it's not let me move to so something that is shown as this purple it's standing wave vibrating and we have two of them on level number two when I have level number three I see three standing waves when I'm on level number four when I have orbit number four I have four standing waves when I have orbit five I have five standing waves Orbit Six standing waves orbit seven seven standing waves and uh what do we know about wave the wave must heat the circum circumference of orbit exactly otherwise otherwise the wave would clean cancel itself so only integral number of waves fitting into circumference of orbits so something like this is possible something like B on V picture V diagram impossible in this case when [Music] um when its circumstance circumstance it doesn't fit properly into orbit and such an orbit not allowed so we can have orbits one two three or five whatever which fit into themselves integral integer so whole number of waves one wave or two ways or three ways or so don't that is why we have restricted certain discrete discrete orbits with discrete Energies so um our electron not on the particle it is wave in this case it's standing wave and the brawl um proposed this formula and this formula connects uh tells us about wave properties of a electron what is who is who in this equation we have a pi which is nothing else but 314 R is radius of orbit and N is n is some number which is one two or three in in um second episode you will see that it is print principle quantum number and uh Lambda is wavelengths okay let us read uh this conclusion which is given in in in in in in here and then we solve the next problem the electron is not a particle located at some point of atom but mass and charge spread out into standing wave surrounding the nucleus Deborah reasoning led to conclusion that waves can behave like particles and particles can exhibit wave-like properties so actually he proposed that any matter in particles can have wave-like properties and here is Formula wavelengths let us solve as problem number three calculate the wavelengths in nanometers associated with electron mass of electron is given and speed of electrons given okay if wavelength is wanted here is also wavelengths is h divided by m and divide by velocity of our electron H is 6 3. by the way can you see that here a different units are are given before we we had unit like Joule multiply by second so here units are different but it's the same constant units are rearranged multiply by 10 in power negative 34 and it is kilograms multiplied by meters in power 2. and divide by second and um our mass of electron 9 11 multiplied by 10 in power negative 31 kilograms and uh speed is 531 multiplied by 10 in power 6 meters per second I want to hug uh something that I have in my denominator okay let's plug numbers stream multiply by 10 in power negative 34 divide parenthesis 9 11 um multiply by negative 31 and multiply by 5. 31 multiplied by 10 in power 6 and I close parenthesis what I have my my number my answer and I give it with three significant figures is 1 37 multiplied by 10 in power negative 10 and it will be meters let us make sure that I have these unit look at this kilograms multiplied by um meters in power two divide by second so this unit I need to divide it by kilogram and I need to divide it by meters per second it can be written as kilograms multiply by meters and Power 2. divide by second multiply by 1 kilograms and multiply by second meters so if I have if I divide by a fraction I need to flip it okay I see that my second second canceled meters in power 2 in meters cancel kilograms kilograms cancel yes I have meters so here is my answer and next piece of information which lead us to to which lead us close and close to structure of atom Heisenberg uncertainty principle and Schrodinger wave equation so our next task is to combine wave-like properties of electron with nuclear model of atom it was a German scientist Werner Heisenberg who tried to locate electron which now we know that it's wave and particle and he was found it is impossible to know both the momentum and momentum can be sought as just velocity and position of particle and of electron at the same time so we cannot know exactly both position of electron and velocity of electron the point is that more we know about position bless we know about about velocity or opposite the more we know about uh velocity the less we know about position and here is actually very nice simulation and basically I I believe that if you if you click on on this link you we will go there so you see that uh if I have large um large uncertainty in my yeah what what is what here so let me see the more precisely you specify position X the less certain you about velocity okay so you see that we have large okay this is simple large uncertainty about position this means that I know a lot about um speed if I know a lot about if I know a lot about uh speed I know I know nothing about place and um this simulation tells us so this area um shows us product off position and velocity so product will be the same but the more I know about position the less I know about velocity okay the Heisenberg uncertain depressed principle made it obvious that there was fundamental Arrow in the Bohr model of the atom since the position and momentum velocity of particle cannot be known simultaneous War theory that electron circled uh traveled in circled paths fixed radius cannot be true theory so who decided to figure out what is going on and he adopted them proposal of Deborah that um electron possesses wave like properties and he formulated wave equation that accurately calculated energy levels of electron in atom so now I show you two models so according needs War model of atom it also known as planetary model so War model of atom or planetary model of Adam we have nucleus we know that in nucleus we have protons and neutrons and electrons move around nucleus in all bits like planets around sun this orbit and this word orbit is important for us is well defined 2D circular path the orbit have fixed energies and fixed sizes and energy of electron quantized so if in exam I ask you who said that energy of electron quantized your answer should be War yeah Schrodinger equations gave us different answer and actually his model uh his equation lead to some model and this model is current model we use it right now we believe that this is truth right now so government Schrodinger model also we call it sometimes electron cloud model says that we have nucleus so nothing happened with that we still have nucleus with protons and neutrons inside but electrons are found in blurry electron cloud and electron clouds are orbitals look at this orbit word orbit is about bore and about current model orbital is electron cloud orbital is volume of space where its highest probability of finding of electron and orbital is 3D shape and please know that orbit which was in historical Niels Bohr model is 2D path so um please know the difference between two models so when Urban Irvin Schrodinger formulated his equation the solutions of his equations were some functions which later where was named as orbitals so orbitals which are probabilities of finding of electrons are solutions of Schrodinger equations Schrodinger equations are difficult and it's not our topic at all for us it's important to know that orbitals are solution from Schrodinger equations orbitals are spaces at uh places at space where there is highest probability of finding of electrons okay I think that we can finish right here