Intensity equation light mcat4/21/2024 ![]() ![]() Times 10 to the eighth meters per second as the speed of light. Over here R would be equal to 2.17, times 10 to the negative 18, over h is Planck's constant, that's 6.626 times 10 to the negative 34, and then c is the speed of light. So, R is called the Rydberg constant so let's see if we can solve for that. Over lambda is equal to negative R times one over j squared minus one over i squared. I'm going to rewrite this as R, so this would be one H is Planck's constant, andĬ is the speed of light, so we have all these constants here. Worry about the negative sign, and just think about what we have. Well let's look a littleīit more closely at what we have right here. We are going to divide by hc,Īnd this is one over j squared minus one over i squared. See that calculation in an earlier video. To E1 was negative 2.17 times 10 to the negative 18 joules. Video, we calculated what that E1 is equal to. Have one over the wavelength is equal to E1 divided by hc, one over j squared minus We could divide both sidesīy hc, so let's do that. Us one over j squared minus one over i squared, like that. So we have hc over lambda is equal to E1, and so that would give We have hc over lambda is equal to Ej was E1 over j squared andĮi was E1 over i squared. I could take all of this, I could take this and IĬould plug it into here. Alright, if I wanted to know the energy for the lower energy level, that was Ei, and that's equal to E1ĭivided by i squared. We could take that and weĬould plug it in to here. So, if we wanted to know the energy when n is equal to j, that Level, n, is equal to E1 divided by n squared. Video, I showed you how you can calculate theĮnergy at any energy level. Level, minus the energy of the lower energy level, like that. Is equal to the energy of the higher energy Let's get some more room, and let's see if we can solve that a So now we have this equation, let me go and highlight it here. The energy of the photon would be equal to the higher energy level, Ej minus the lower energy which is Ei. Let's make it more generic, let's do Ej and Ei. To a lower energy level, which we'll call Ei. Let's call this Ej now, so this is just a higher energy level, Ej. Instead of using E3 andĮ1, let's think about a generic high energy level. Now we have the energy of the photon is equal to hc over lambda. I'll write that in here, times the frequency, and We get the energy of a photon is equal to Planck's constant, h, Then, we're going to take all of that and plug this in to here. So, if we solve for the frequency, theįrequency would be equal to the speed of light divided by lambda. Lambda is the wavelength, and nu is the frequency. The equation that does that is of course, C is equal to lambda nu. We need to relate theįrequency to the wavelength. Let me go ahead and write that over here. This is equal to theĮnergy of that photon here. That's equal to the energy of the photon. So, the energy of the third energy level minus the energy of We have energy with the third energy level and the first energy level. The energy of the photon is, the energy of the emitted photon is equal to the difference in energy between those two energy levels. We need to figure out how to relate lambda to those different energy levels. We emit a photon, which is going to have a certain wavelength. When the electron dropsįrom a higher energy level to a lower energy level, it emits light. Here's the electron going back to the first energy level here. It's eventually going to fallīack down to the ground state, the first energy level. Here's our electron, it'sĪt the third energy level. It's eventually going to fallīack down to the ground state. This is only temporary though, the electron is not going The electron absorbs energy and jumps up to a higher energy level. So now this electron is a distance of r3, so we're talking about the If we add the right amount of energy, this electron can jump up ![]() That if you apply the right amount of energy, you can So this electron is in the lowest energy level, the ground state. Negatively charged electron a distance of r1, and If you're going by the Bohr model, the negatively chargedĮlectron is orbiting the nucleus at a certain distance. 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 ![]()
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