 So, we have understood that there is something weird going on when it comes to the atoms. So, there is one more weird thing about the electron revolving around the nucleus that is came up after Maxwell proposed his theory, according to Maxwell whenever charge accelerates it will emit E m wave. Now, electron if it is moving around the circular path it is accelerating right. So, it will emit E m wave fine. So, this electron that is moving in the nucleus like this will emit E m wave. So, if this emits E m wave what will happen to its energy? Energy decreases will go down. So, energy should go down for the electron right and what is the formula for energy of an electron minus 1 by 2 1 by 4 pi epsilon naught e square by r fine. Now if energy decreases what happens to the radius what will happen to the radius? Decrease or increase? Decrease right, suppose this is right now minus 5, this is a negative quantity no doubt suppose it is minus 5. If minus i have to decrease what it should become minus 6 or minus 7 and if it has to become minus 6 the r should be less. So, that this is more negative fine. So, electron if it is emitting E m wave its radius should decrease and slowly and slowly it should spiral and come and hit the nucleus like this. Why earth does not do like this? Because earth has no charge it is happening because of gravity fine. But according to Maxwell if charge accelerates it will emit E m wave. So, if Maxwell has to be correct according to that the electron should revolve and spiral into the nucleus but that is not happening fine. So, another weird observation. So, hence there was a requirement of a different kind of physics that could explain what is happening because nobody is able to explain what is going on. So, Bohr came up with quantum physics to explain what is going on fine. Bohr has proposed hydrogen atoms model and he has given three postulates when it comes to hydrogen like atom. So, we will first talk about three postulates or three principle on which the hydrogen atom works right down the first one electrons can revolve in certain stable orbits without emitting. So, he started with this that he was like if there are certain stable orbits electron if it revolves around those stable orbit it will not emit E m wave even if it is accelerating fine. So, the second postulate right down for these stable orbits for these stable orbits how you identify these the angular momentum should be quantized angular momentum of electron is quantized. What is the angular momentum of a mass moving in a circular orbit m v i m v which is a linear momentum cross width. The thing is this is the electron's path fine this is the velocity. So, its momentum is also along this line. So, perpendicular distance of the momentum from the center is radius only. So, m v into r is the angular momentum fine. So, basically m v r when this is equal to n h by 2 pi. If an orbit satisfies this equation if orbit satisfies this equation then that is a stable orbit. So, electron can be in that stable orbit without emitting E m wave, but if it is not in the stable orbit then what will happen then it will emit E m wave and it will reduce its radius and go to the next possible stable orbit third postulate. Electron can jump from one stable orbit to another stable orbit by emitting or absorbing a photon the focus is a photon. It cannot absorb more than a photon more than a single photon it cannot only one photon it can absorb. So, by absorbing or emitting a single photon whose energy is difference in the energy of those stable orbits. So, if energy of one stable orbit is even other is E 2 even is more than E 2 fine. Let us say energy of one orbit is even and other is E 2 and even is more than E 2. So, if it is jumping from even to E 2 it will emit or absorb photon emitting and it is going from E 2 to E 1 absorb how much energy E 2 minus E 1 or E 1 minus E 2 right and that should be energy of a single photon it cannot be that that energy is coming from two different photons fine. So, there is a fixed wavelength it can absorb which is corresponding to the energy difference and there is a fixed wavelength it can emit that is why it emits or absorb only fixed number of what is revivalence are you getting it any doubt on this three postulate no. Now, you will see that whatever was the experimental observation will be able to use these postulate to match and you will see that both are match for example, let us take postulate number 3. According to postulate number 3 energy of the photon should be equal to let us say this is h times mu this should be equal to what E 2 minus E 1 fine. So, mu is what C by lambda this is E 2 minus E 1 for the electron right. So, 1 by lambda becomes what 1 by lambda is 1 by h into C. Now, E 2 is what E 2 is minus half this is total energy minus half 1 by 4 pi epsilon naught E square by E square by let us say it is R 2 square sorry R 2 only fine minus of minus 1 by 2 1 by 4 pi epsilon naught E square by R 1 square getting it fine. So, R 1 and R 2 are what radius for energy level 2 and energy level 1 fine, but then there are no integer coming up right now getting it. So, just keep it like this we will come back to this expression once we are able to derive R 2 and R 1 in terms of an integer. Now, tell me if this is the second postulate if n v r is equal to n h by 2 pi can you tell me what is the total energy I do not want energy in terms of r I want energy in terms of n n you have one more equation. So, you can put the energy in terms of n v square by r that is 4 equation is still valid n v square by r is equal to k q 1 q 2 by r square that is valid and this also is valid. So, you have two equations to play with find out total energy equal to are you able to or should I do it ok. See we have this equation n v square by r is equal to what I will just write k here k times e square by r square this we have right. So, one r we get cancel. So, I will get m into v square is equal to k times e square by r fine. Now, continuity is very easy to find you can just multiply half to it will get continuity this which you have already found earlier itself fine, but then I want kiting energy to be in terms of n or total energy in terms of n fine. In order to do that I will square this equation let me square it I will get m square v square r square is equal to n square h square by 4 pi. So, I will get m v square is equal to n square h square divided by 4 pi square m into r square this is what we will get. So, you will get half of this is equal to that fine, but it is in terms of r only you have this second equation. If you equate them if you equate them you will get the value for r this is equal to n square h square divided by 8 pi square m r square. So, I will just expand k also now this is 1 by 4 pi epsilon naught. So, 1 pi will get cancelled 4 to the 8 1 r will get cancelled. So, r will come out to be n square h square by n square h square epsilon naught by pi m. So, this is what I will get. So, I will get n square e square fine this is r. Now, when you substitute that r there you will get the kiting energy. So, kiting energy will be what equal to 1 by 4 pi epsilon naught that is k into e square divided by 2 times r which is n square h square epsilon naught divided by 2 pi m e square pi will go away this is 2. So, you will get m e to the power 4 divided by h square epsilon naught 2 times of that epsilon naught square in fact. So, this is equal to 1 by n square fine. So, this is kiting energy all right what is the total energy minus of this minus of this. Let me just verify whether we have made correct calculation in power 4 there is a factor of 8 coming in the denominator which we have got kiting energy is this only right k e square by 2 r will be 2 coming in. So, this is 8 this completely goes away. So, this is gone this will be 4 anyways. So, we have made some cylinder somewhere this is actually 8 a factor of 8 will come here somewhere we have made a cylinder here. So, we have total energy is what this is kiting energy. So, total energy should be negative all this fine this is kiting energy. So, total energy should be equal to minus of m e to the power 4 divided by 8 h square epsilon naught square into 1 by n square. So, instead of e to n even I can substitute that fine rather than putting it in terms of radius I can put in terms of n where n is not principal quantum number that is an integer fine. So, if you put it here you will get e to which is minus of m e to the power 4 divided by 8 h square epsilon naught square into 1 by n 2 square take that common will be 1 by n 1 square fine. So, if you put minus inside if you take minus inside this thing will become n 1 and this will become n 2 fine and then this whole thing this this and this will become a Littberg constant when you put the values you get the same thing 1 by lambda is a Littberg constant 1 by n 1 square minus 1 by n 2 square where n 1 is less than n 2 fine always this remember it is this n 1 which determines what series it is the lower number if the electron jumps from 3 to 2 which series it is? If it goes from 2 to 4 what it is? lower number determines what series it is. So, now we have a model based on which we can understand what is going on in hydrogen or hydrogen like atom for hydrogen like atom the same formula becomes like this 1 by lambda is equal to Littberg constant into z square 1 by n 1 minus 1 by n 2 square this is for hydrogen like atom having atomic number more than 1 I think it and you can arrive here easily when you write this equation m v square by r if it is higher atomic number what you write here 1 by 4 pi epsilon naught q 1 is now z times e and this is e divided by r square and m v r is still equal to n h by 2 pi. So, if you start like this you will get it here. So, you will you will be able to find out radius in fact we have found radius first in terms of n it is proportional to n square energy is proportional to 1 minus 1 by n square you getting it similarly you can get velocity. So, now let us try to find out the energy corresponding to nth level we have derived an equation right how much that was equal to minus of energy in the nth all way how much this was minus m e to the power 4 divided by h square epsilon square into 1 by n square. So, when you substitute all the values you will get energy in the nth orbit to be 13.6 divided by n square electron volt in terms of joule how much this will be into charge of electron. So, energy in the nth orbit is this and if you take that third postulate post third postulate simply you have to do this you know minus 13.6 n 1 square minus of minus 13.6 n 2 square this is delta e change in energy that should be equal to h c by lambda of course, this should be multiplied with charge of electron e getting it e 2 minus e 1 sorry e 2 minus e 1 should come n 2. So, e 2 minus e 1 is equal to h c by lambda same thing we have written fine. So, the Leimer-Bahmer passion and everything was just experimental finding you can use that whenever they ask you to find out the wavelength you can use that readymade formula 1 by lambda is written constant everything else fine. Suppose they ask you to find the energy you can use this and suppose you are confused what to do then use this this is safe as well because you are going by logic here.