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# Absorption and emission

## Video transcript

we've been talking about the Bohr model for the hydrogen atom and we know the hydrogen atom has one positive charge in the nucleus so here's our positively charged nucleus of the hydrogen atom and a negatively charged electron and if you're going by the Bohr model the negatively charged electron is orbiting the nucleus at a certain distance and so here I put the negatively charged electron a distance of R 1 and so this electron is in the lowest energy level the ground state so this is the first energy level e 1 we saw in the previous video that if you apply the right amount of energy you can promote that electron the electron can jump up to a higher energy level and so if we add the right amount of energy this electron can jump up to a higher energy level and so now this electron is distance of R 3 so we're talking about the third energy level here and this is the process of absorption the electron absorbs energy and jumps up to a higher energy level this is only temporary though the electron is not going to stay there forever it's eventually going to fall back down to the ground state and so let's go ahead and put that on the diagram on the right and so here's our electron alright it's at the third energy level it's eventually going to fall back down to the ground state the first energy level so here's the electron going back to the first energy level here and when it does that it's going to emit a photon all right so it's going to emit light so when the electron drops from a higher energy level to a lower energy level it emits light this is the process of emission and I could represent that photon here this is how you usually see it in textbooks so the we emit a photon which is going to have a certain wavelength right lambda is lambda is the symbol for wavelength and we need to figure out how to relate lambda to those different energy levels all right so the energy of the photon is the energy of the emitted photon is equal to the difference in energy between those two energy levels so we have energy with the third energy level and the first energy level all right so the difference between those so the energy of the third energy level minus the energy of the first energy level that's equal to the energy of the photon this is equal to the energy of that photon here and we know the energy of a photon right energy of a photon is equal to H nu so let me go ahead and write that over here energy of a photon is equal to H nu H is Planck's constant this is Planck's constant and nu is the frequency alright but we want to think about wavelength so we need to relate the frequency to the wavelength and the equation that does that is of course C is equal to lambda nu so C is the speed of light lambda is the wavelength and nu is the frequency and so if we if we solve right if we solve for the frequency the frequency would be equal to the speed of light divided by lambda and then we're going to take all of that right and plug this in to here and so we get the energy of a photon is equal to Planck's constant H and write that in here x times the frequency and the frequency is equal to C over lambda so now we have the energy of the photon is equal to HC over lambda and instead of using a 3 and E 1 let's think about a high energy level so let's uh let's call this let's call this e J now so this is just a higher energy level e J and the electron falls back down to a lower energy level which we'll call e I so instead of using III and E 1 let's let's make it more generic let's do a J and E I so let's go ahead and plug that in now so the energy the photon would be equal to the higher energy level right II J minus the lower energy which is e I and so now we have this equation let me go and highlight it here so we have we have HC over lambda is equal to EJ minus e I and let's get some more room and let's see if we can solve that a little bit better here so let me write this down here so we have HC over lambda is equal to the energy of the higher energy level minus the energy of the lower energy level like that alright so in an earlier video I showed you how you can calculate the energy at any energy level and we derive this equation so the energy at any energy level n is equal to e 1 divided by N squared so if we wanted to know if you want to note the energy right when n is equal to J well that would just be e 1 over J squared and so we could take that we could take that and we could plug it in to here all right if I wanted to know the energy for the lower energy level that was e I all right and that's equal to e 1 divided by I squared so I could take all of this right I can take this and I could plug it into here so let's once again get some more room and let's write what we have so far we have H C over lambda is equal to e J was e 1 over J squared and E I was e 1 over I squared ok we could we could pull out an e 1 on the right so we have HC over lambda is equal to e 1 and so that would give us 1 over J squared minus 1 over I squared like that and we could we could divide both sides by HC so let's do that so on the left we would have 1 over the wavelength is equal to e 1 divided by HC 1 over J squared minus 1 over I squared and again from an earlier video we calculated what that e 1 is equal to so 1 over lambda is equal to e 1 was negative 2 point one seven times ten to the negative 18 joules so once again you can see that calculation in an earlier video it took us a while to get there and we are going to divide by H C and this is one over J squared minus one over I squared well let's look a little more closely at what we have right here so if I right now not worry about the negative sign and just think about what we have right we this is all equal to a constant all right because H is Planck's constant and C is the speed of light and so we have all these constants here and so we could we could rewrite all of these as just R so I'm going to rewrite this as R since be 1 over lambda is equal to negative R times 1 over J squared minus 1 over I squared so R is called the rib burg constant so let's see if we can solve for that so over here R be equal to two point one seven times 10 to the negative 18 all right over H is Planck's constant that's six point six two six times 10 to the negative 34 and then C is the speed of light and so we could use two point nine nine seven nine times ten to the eighth meters per second as the speed of light and if you do all that math all right if you do that math I won't do it here to save time but if you do all that you'll get one point zero nine times ten to the seventh and this is a one over meters and I think I might have it's possible I had rounding I had a rounding issue in here because if you used 2.18 you get a better number it's one point zero nine seven times ten to the seventh which is the rid Burgh constant and so this uh this is just again I'm just trying to show you the idea behind the Redbird constant here so we get this value for the Redbird constant and so you could you could plug that in for R if you needed to and we're going to be doing that in the next video so you could stop right there and and and you have related the wavelength right to your different energy levels or you could go a little bit further let's just go a little bit further here so one over lambda is equal to negative R if we pull out a negative one if you pull out a negative one that would give us 1 over I squared minus 1 over J squared so we now we have these two negative signs right these two negative signs out here which gives us a positive so this is now equal to 1 over lambda 1 over the wavelength is equal to positive R the Redbird constant times 1 over I squared minus 1 over J squared and remember what I and J represented right I represented the lower energy level right and J represented the higher energy level and so this is an extremely useful equation so usually you see this called the Balmer Rydberg equation and we've derived this equation using the assumptions of the Bohr model and this equation is extremely useful because it explains the entire emission spectrum of hydrogen and this is again this is why we were why we're exploring the Bohr model in the first place so we got this equation and in the next video we're going to see we're going to see how this explains the emission spectrum of hydrogen so think about think about lambda or the wavelength right as the as the light that is emitted when the electron falls back down to a lower energy State
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