 So, we have briefly understood about how electrons should behave, okay. Now in previous chapter we have understood electron as a wave, fine. In this chapter we are trying, we are treating electron as a particle, it is just a particle it is moving in a circle. So once this electron was discovered and the items and everything the model properly is in place then you know more and more experiments are conducted to understand the exact behavior of the electrons, fine. So do you know black body radiation? So if there is a black body it will be able to absorb every wavelength that is falling on it and should be emitting every wavelength possible. So if you draw a graph between energy for a particular wavelength and that is this is intensity and the wavelength you will get a graph like this, are you getting it? So for a solid every wavelength has some intensity almost every wavelength is present, getting it? But for the gases it is not like that, okay. The issue with the solid is this that the atoms are able to interact with each other, there is a potentiality also in place. So it is not just about a single atom, it is also about how one atom interact with the other atom, there is a lattice in place, so there is a vibration that vibration can also create a wavelength, right. So when you study solid you cannot say that this is the behavior of an atom, only atom, this is a collective behavior, how the atoms interact among themselves also, fine. But when you study gas, fine, we can ignore the force of attraction between the two atoms, okay. Then whatever happens will be the atomic property, the behavior of the atom only, okay. So similar kind of spectrum was being studied on hydrogen gas, okay and the observation were completely different, so just like blackbody absorbs and emits every wavelength similarly they were trying to see how, I mean what are wavelengths or how the gas will absorb the wavelength and how gas will emit the wavelength, okay. So since it is only because of the atoms when it comes to gas, we also call it atomic spectrum. Now there are two kinds of atomic spectra, emission and absorption, simple, okay. So suppose you take a tube, you can take a transparent tube like this, here you put the gas, okay, you put the hydrogen gas in it and suppose you are passing multiple wavelengths through it, there are multiple wavelengths, all sorts of wavelengths, there is a range of wavelength between lambda 1 to let us say lambda 10, okay, 10 wavelengths you have passed, alright. What is seen here is that only couple of wavelengths are able to come out, for example from here only let us say lambda 3, lambda 5 and lambda 7 comes out, okay. The other wavelength get absorbed in the gas, fine and these wavelengths are not even absorbed, they are just rejected, are you getting it, fine. So this is for the hydrogen gas, so hydrogen gas you pass lambda 1 to lambda 10, it absorbs lambda 1, lambda 2, lambda 4, lambda 6, lambda 8, lambda 9, lambda 10, fine. Suppose you replace hydrogen gas with nitrogen gas, then it may absorb lambda 2, lambda 5, lambda 7, lambda 3, right. So there are different wavelengths each gas absorbs and this should be the property of the atom, getting it, this kind of behavior is not seen in blackbird or any of solid object, whatever you throw on it, it will absorb, but gas doesn't, getting it, like for example in photoelectric emission, we had different wavelength falling on the metallic surface, it will absorb all the wavelength, electron may not be able to come out for all the wavelengths, but then it will absorb. So absorption spectrum for solid is straight forward, it absorbs everything that falls on it, fine, until and unless it is like purely reflective surface or something like that, okay, but the gas selectively absorbs and one gas may absorb different wavelength, other gas may absorb some other wavelength. So this kind of spectrum, the spectrum of wavelength it absorbs, it is called absorption spectrum, getting it, you can in fact plot a line like this and these lines may represent what wavelength it is absorbing, you can say that, this is an axis through which the wavelengths are changing, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, like that, so this is like a bar code, okay, these wavelengths it will absorb and every gas has a different type of bar code, getting it, so that is the reason why this can be used as a signature of the gas, just like signature of a gas, you can identify which gas is present by using this sort of setup, fine, this is absorption spectrum, there is also something called emission spectrum, just like blackbody, okay, the emission spectrum is like this, suppose you give energy to it by some means, fine, so it will selectively absorb the wavelengths or photons, whatever it has to absorb, right, then the gas will become exalted, fine and after that if you let it cool or if you let it do whatever it wants, then it will go to the ground state or it will de-excite and when it de-excites, it will throw away some wavelengths in the form of photons, fine and when it is throwing away the wavelengths in terms of photons, they are also some selective wavelengths, they are not all the wavelengths possible, they are fixed, fine, so this is emission spectrum, so there also is a bar code sort of thing and this emission spectrum matches with absorption spectrum, so whatever wavelength it absorbs, similar wavelength or same wavelength, it emits, fine, this is the first observation when it comes to how atoms behave, because study of gas will give you more insight towards the atomic behavior than study of a solid, because every atom is independent in the gas, fine, so this sort of experiment created lot of issues, like you know it was never expected that it would behave like this, why it is selectively absorbing, why it is selectively emitting, fine, so people started asking questions, fine, so for several years there was no answer, there was no answer several years, but then during that time people have systematically started to understand, okay, how this wavelength get emitted, I am not how as in what is the wavelength that get emitted, you know, is there any formula as such which they can have you ever derived a formula using graph, y is equal to mx plus c used to fit the curve, right, similar sort of thing people started to do, they know that what wavelength is coming out for what atoms, so they started plotting the graph and they started to see what is the pattern, can they derive some formula out of it without knowing why it is happening, fine, so such kind of effort was going on, because it was taking lot of time for any explanation to come up, so let us talk about that now, right on spectral series, okay, so when the first, when the first observation was made on spectral series as in the different kinds of wavelength, the first what kind of wavelength do you think will be getting observed, the visible wavelength, fine, so the person who have studied this particular wavelength from the hydrogen atom, the name of that person is Bummer, fine, Bummer was a school teacher, he had less access to any sophisticated machine or anything that can read the wavelength which are beyond the visible spectrum, fine, but then there was good enough instrument to actually detect what kind of visible spectrum wavelength is there in that school, so he studied that, that is why you call Bummer series, okay, so what Bummer has done, he has found out a formula for the wavelength that will get absorbed or emitted in hydrogen gas, getting it, fine, in hydrogen gas what are the wavelength that gets absorbed or emitted, that is what Bummer have derived, Bummer thought that he has derived all the wavelengths, why, because he could not observe other wavelengths other than the visible spectrum, fine, so what Bummer has derived is this, 1 by lambda is a constant 1 by 2 square minus 1 by n square, where n is greater than 2, it has to be greater than 2, wavelength can't be negative, getting it, the value of this constant, first of all this is called Ritberg constant, R H is Ritberg constant whose value is what, 10967, sure, units, this is dimensionless, 1 by lambda is the unit of this, meter inverse, that is not correct, it is 1.097 into 10 square 7, here you see 10 square 7, here you see 5 is coming, this is the centimeter inverse, in physics we are mostly dealing with the SI units, so let's put it like this, 1.097 into 10 raise to power 7 meter inverse, this is what, Bummer series, why it is called series, I mean is there any limit between which this Bummer's wavelength is bounded in, is there a maximum wavelength or minimum wavelength for Bummer series, how do you find minimum wavelength, how do you find minimum, for minimum wavelength 1 by lambda should be, if lambda is minimum, 1 by lambda should be maximum and when 1 by lambda is maximum, the value of this should be maximum and when this is maximum, when n is infinity, this is maximum, when you don't subtract anything, this is anyway a positive quantity, the minimum value of this is 0, when n tends to infinity. So, right now for lambda minimum, this is 1 by lambda should be maximum, it implies n tending to infinity, so you will get 1 by lambda minimum is equal to ribbock constant divided by 4, right again, how do you find lambda maximum, what is the maximum possible wavelength, for lambda maximum 1 by lambda should be minimum and for that, this should be minimum and what is the minimum value of this, when you put n equal to 3, how you put n equal to 1, there is a negative, right, n should be greater than 2, so when you put n equal to 3, you will get lambda maximum, so lambda maximum when n is equal to 3, so it has a limit between lambda minimum and lambda maximum, barma series lies, right, this is barma series, so once barma has discovered these formulas, then there are other people also who have contributed, okay, there are several people, okay, this Lyman is their bracket, pasture, barn, okay, for Lyman, now you can find out lambda minimum, lambda maximum for all the series, right, for Lyman, we have 1 by lambda equal to ribbock constant multiplied by 1 by 1 square minus 1 by n square, where n is greater than 1, so this is Lyman, then you have, what is this, 1 by 3 square minus 1 by n square, this is n greater than 3, this is what, this is pasture, after Lyman barma comes, Lyman, barma, pasture, bracket, barn, Lyman, barma, pasture, right, then 1 by lambda, ribbock constant, 1 by 4 square minus 1 by n square, this is bracket, 1 by lambda, ribbock constant, 1 by 5 square minus 1 by n square, this is fun, fine, see the thing is the list can go on and on, you can have now n equal to 6, right, but then after n equal to 5, you will see the range shrinks between lambda minimum and maximum, so very few we have left, okay, so that is why we stop at fun, but n can go till infinity also, now till now all this is experimental stuff, people have done some experiment, came up with an observation using graph or something like that, they are able to come up with this expression, okay, but nobody had till now, I mean not till now, that is, they are given any explanation to it, fine, so Neil Bohr, who is like the father of quantum physics, he came up with the explanation of what is happening.