a neutron walks into a bar and asks how much for a drink and the bartender replies for you no charge that's such a bad joke but I love it so we're going to talk about nuclear physics and energy levels um and it's important to talk about uh different ways of notation I think once you understand this it's going to make all the rest of this topic a lot easier so first of all the very simple simple atom I put that down because it's just I mean it's so ridiculously simple we know now the atom is not really this simple but for now it suffices to say this so inside an atom there's a central nucleus that's why we call it Nuclear Physics right um we've got neutrons inside and we've got protons inside that's what n and p means and of course in orbit we have um electrons we're not going to care so much about the electrons for now by the way I've made the um the nucleus extremely big obviously there's a lot of space in an atom it's almost all space right so just keep in mind we got number of neutrons and protons in the center so that's in the nucleus that's the part we're going to be mainly concerned with for now um and it's important to talk about the notation so this would be some general uh whoops actually I probably shouldn't say a I should probably actually say x instead um I think it's maybe better to say that so I'm going to replace it with uh something like X this is just like some element doesn't matter what it is so we normally use Zed and this Zed like this bottom number right here um and I'll give you some examples like over here um normally we write this bottom number here we call this the atomic number and the reason we call it that is because it's the number um of protons so this would be the number of protons in the nucleus this is the key thing here with this Zed or this atomic number so that'll tell you the number of protons so for example this one right here h e that's helium and you know that there's two protons then this top number right here is called the mass number and the mass number tells you the number of nucleons so you might wonder what's a nucleon nucleon is just a particle in the nucleus in other words it's equal to n plus p in other words the number of neutrons plus the number of protons so in this case right here for example with helium we've got two protons and we've got four nucleons now two of them are already protons so two four - 2 is 2 so that's how we know there are um let's just say two neutrons then we can say there's two neutrons in here here there's two protons and this is how it works okay this is the notation that we use the important thing is that the element name for example helium and that bottom number the atomic number they're redundant what I mean by redundant is that uh you don't need them you could just say helium and you know it's two because this bottom number tells you which element on the periodic table it is so now we know that helium is a second element you know we know that hydrogen is the first and it's this top number that might vary but not the bottom number so they're redundant that's why we often call this helium 4 we don't have to say helium two for because this two on the bottom is redundant saying helium we know it's got to be two as soon as you make it number three it's the next element it can't be helium more interesting then is the energy levels so what happens is in an atom uh you've got of course those nucleons in the center the neutrons and the protons and Around It Go these electrons those electrons are important um as far as these energy levels because what will happen is they can get excited by maybe they for example absorb a photon uh or maybe you apply a potential difference across them that's what happens in like a lot of those um fluorescent lights for example in a room maybe the room you're sitting in has fluorescent lights in it right now so if you look at that what happens is you end up taking um electrons and you excite them into what we call an in excited state so I could maybe draw that I could draw myself like some line like this right here and another line like this maybe another line like this I'm just trying to draw some parallel lines here I'm doing a bad job of it but there we go what'll happen then is these electrons maybe it goes all the way up to the very top and what happens is this when they drop down an energy so for example uh right here so maybe so now it's in an excited state and maybe now it drops down like this right here to that energy level when it did that it's going to emit a photon it's going to emit some light so we normally write that with a curvy line we could say it's a photon and that Photon will have a very specific energy this is the key thing here with this it goes eal HF this is the key equation here that you need for this stuff here this is on your data booklet so you don't have to memorize it but it goes E equals HF where e is the energy of the photon now that could be in Jewels but we normally do the energy in EV so of course you can do in Jews or you can do electron volts H is just a constant you look it up what is it 6.63 * 10us 34 so it's called planks constant uh and what's important is this energies that we find of photons for example the energy is quantized what I mean by quantized means it only comes in multiples of H you can have 2 H or 3 H or 4 H but it's always a multiple of this sort of magical number this Plank's constant then we have f is the frequency of the photon and remember frequency is measured in hertz or could be in uh seconds to Theus one that's the same thing as a Hertz now keep in mind there's a lot of other energy levels uh transitions possible so can you notice it could have dropped here then it could drop down two of these or it could go down here then it could go down here you see there's a lot of different combinations it could also drop from let's just say we kept going here it could also drop from here to here um it could drop all the way down in one go so do you see there's a lot of these different energy levels Poss possible and each of those energy levels do you see this this this difference in energy here you'd have to actually measure it whatever that distance is that's e so then you know the type of photon you're going to get because that tells you the frequency of the photon it's Unique so for example this one right here will have a very different energy than that one right there right because this one has a much larger energy and a larger energy means a larger frequency Photon so this is really important this basically tells you the different colors that are possible because you know the frequency of a photon is its color in a sense even if it's even if you can't see it uh but I me it really tells you that the frequency is related to its wavelength so so if you ever get a question like this you have to think of all the different transitions possible you know so from the top you can go down all the way to the bottom you can go down until the second last one like I did you can go down just that one and then from here you can go all the way down or one in one uh so this is how it works I I hope this is clear because of course you can always raise and drop by lots of different things but this is actually what explains the uh quantized nature of this light in other words you won't have every frequency possible you only have these specific allowed frequencies uh so that's really important now if you want you can also translate to sort of rewrite this equation because we have this equation here eals HF uh but we also have the equation we called the wave equation you know some people we call it v = f Lambda if it's light we say C equals F Lambda so that's the speed uh equals the frequency times the wavelength if you want to do that we could replace for f we can get F by itself so that would be C over Lambda that means then we can rewrite this equation which when eal HF we can say eal h and instead of f we put in Cal Lambda and from there then we can take Lambda put it over here to this top here so we can say Lambda equals and it's HC over e and that's where that equation right there came from this is just a different version of eal HF this is it relating to wavelength so if you want the wavelength of the photon there you go and a nice easy thing to remember is that frequency and wavelength do opposites so if you have a large frequency for example uh this transition right here has a very large frequency because it has a very large energy well then it's going to have a very small wavelength because they work opposites to each other maybe that that's a good idea to do this example this is from an exam so something like this electrons in an atom are excited and they have a following energy levels possible when they go down in energy of course there's other ones possible but I'm just drawing these four to choose from so which of the transitions has the smallest wavelength so if you think about this one now uh let's see what do we want here remember eal HF and if we have smallest you have to remember this okay so smallest we're looking for the smallest wavelength right that means it's the largest frequency this is a key thing to remember here is that if we want the smallest wavelength we want the largest frequency and if we have e equal HF that means then we want the largest energy we want the largest energy value so which one has the largest energy can you see how easy it was it was a so again just to explain it remember um E equals HF so that tells you the energy of the photons is related to the frequency they want the smallest wavelength and frequency of wavelength were opposite to each other so if we want the small Lambda then we want the largest F and since E equals HF the largest f is found by the largest e that's why we want the largest energy not so bad huh