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# Bohr model energy levels

## Video transcript

so in the last video I showed you how to get this equation using a lot of physics and so it's actually not necessary to watch the previous video you can just start with this video if you want and E one we said was the energy associated with an electron and the lowest energy level of hydrogen and we're using the Bohr model and we calculated the value for that energy to be equal to negative two point one seven times ten to the negative 18 joules and let's go ahead and convert that into electron volts it just makes the numbers easier to work with and so one electron volt is equal to one point six times 10 to the negative 19 joules so if I take negative two point one seven times 10 to the negative 18 joules I know that for every one electron volts right one electron volt is equal to one point six times ten to the negative 19 joules and so I have a conversion factor here and so if I multiply these two together the joules would cancel and give me electron volts as my as my unit and so if you do that math you get negative thirteen point six electron volts so once again that's the energy associated with an electron in the lowest energy level in hydrogen and so I plug that back into my equation here and so I could just rewrite it so this means the energy at any energy level n is equal to e 1 which is negative thirteen point six electron volts and we divide that by N squared where n is an integer so 1 2 3 and so on so the energy for the first energy level alright we already know what it is but let's go ahead and do it so you can see how to use this equation is equal to negative 13 point 6 divided by so we're saying the energy for the support n is equal to 1 so whatever number you have here you're going to plug in here so this would just be 1 squared all right which is of course just 1 and so this is negative 13 point 6 electron volts so we already knew that one let's calculate the energy for the second energy level so e to this would just be negative thirteen point six and now n is equal to 2 so this would be 2 squared and when you do that math you get negative three point four electron volts and then let's do one more so the energy for the third energy level is equal to negative thirteen point six now n is equal to three so this would be three squared and this gives you a negative one point five one electron volts so we have the energies for three different energy levels the energy for the first energy level is equal to negative thirteen point six e 2 is equal to negative three point four and III is equal to negative one point five one electron volts so energy is quantized using the Bohr model so you can't have a value of energy in between those energies and also note that your energies are negative and so this turns out to be the highest energy because this is the one that's closest to zero so III is the highest energy level out of the three that we're talking about here all right let's just let's uh let's talk about the Bohr model of the hydrogen atom really fast and so over here on the Left right just just to remind you I already showed you how to get these different radii for the Bohr model so this isn't drawn perfectly to scale but if we assume that we have a positively charged nucleus which I just marked in red here so there's our positively charged nucleus we know the electron orbits the nucleus in the Bohr model so I'm going to draw a little n electron here so again not drawn to scale orbiting the nucleus so the positively charged nucleus attracts the negatively charged electron and I'm saying that electron is orbiting at r1 so that's this first this this first radius right here so r1 is when n is equal to one and we just calculated that energy when n is equal to one that was negative thirteen point six electron volts that's the energy associated with that electron as it orbits the nucleus and so if we go over here on the right and we say this top line here represents energy is equal to zero then this would be negative thirteen point six electron volts so none of this is drawn perfectly to scale but this is just give you an idea about what's happening so this is when n is equal to one the electron is at a distance R one away from the nucleus we're talking about the first energy level and there's an energy of negative thirteen point six electron volts associated with that electron all right let's say the electron was located a distance R two from the nucleus all right so that's n is equal to two and we just calculated that energy is equal to negative three point four electron volts all right and then let's say the electron was at R three from the nucleus that's when n is equal to three and once again we just calculated that energy to be equal to negative one point five one electron volts and so it's useful to compare these two diagrams together because we we understand this concept of energy much better for example let's say we wanted to we wanted to promote the electron that I drew so this electron right here I just marked I just marked let's say we wanted to promote that electron from the lower energy level to a higher energy level so let's say we wanted to add enough energy to cause that electron to go from the first energy level to the second energy level so that electron is jumping up here to the second energy level we would have to give that electron this much energy so the difference in energy between our two energy levels so the difference between these two numbers and if you're thinking about just in terms of magnitude all right thirteen point six minus three point four all right so this is a magnitude of 10.2 electron volts and so if you gave that electron 10.2 electron volts of energy right you could cause that electron to jump from from the first energy level all the way here to the second energy level but you would have to provide the exact right amount of energy in order to get it to do that all right let's say you wanted to cause and the the electron to jump let's say from the first energy level all the way to the third energy level right so from the first energy level to the third energy level so that would be here's our electron in the first energy level let's say we wanted to cause it to jump all the way up to here alright so once again you would have to you have to provide enough energy in order to do that so just thinking about the magnitudes right this was negative one point five one this was negative thirteen point six we just take thirteen point six minus one point five one right we would get we would get how much energy we need to put in in order to cause that transition and so this would be twelve point zero nine electron volts and so if you gave an electron twelve point zero nine electron volts you could promote it to a higher energy level and then finally the last situation let's think about taking the electron alright let's take let's think about taking the electron let me go ahead and draw it in here once more in the first energy level let's say you provide it with enough energy to to take it an infinite distance away from the nucleus so again not drawn to scale so let's say we're at an infinite distance away from the nucleus if the electron is infinitely away from the nucleus it feels no attractive Pole so there's no force there's no attractive force we talked about Coulomb's law earlier so this is when this is when this is when R is equal to infinity here and if there's no attractive force there is no potential energy so the way we define potential energy electrical potential energy its equal to zero when when when R is equal to infinity so the electrical potential energy is equal to zero and if it's not moving that's kinetic energy is equal to zero and therefore its total energy is equal to zero so this is what the diagram over here on the right means so when e is equal to zero we're talking about the electron being an infinite distance away from the nucleus so we could say n is equal to infinity right R is equal to infinity and if it's not moving it has a total energy equal to zero so we've taken the electron completely away from the nucleus we have ionized it alright so we've gone from a neutral hydrogen atom to the hydrogen ion so this turns it into H+ so we're going from H alright we're going from H to H plus and that amount of energy let me use a different color here so obviously requires a lot of energy in order to do that so that would be that would be going from electron here to an electron here so what is what is the magnitude of that energy difference that's thirteen point six electron volt so it takes thirteen point six electron volts to take an electron away from the attractive pole in the nucleus and to turn it into an ion and this number thirteen point six electron volts corresponds to the ionization energy for hydrogen and so the Bohr model accurately predicts the ionization energy for hydrogen and that's one of the reasons why it's useful to study it and to think about these different energy levels so not only are the radii quantized and I just going back over here not only are these radii quantized but the energy levels are too