Over r" is our expression for the total energy. The total energy is equal to: 1/2 Ke squared over r, our expression for the kinetic energy, and then, this was plus, and then we have a negative value, so we just write: minus Ke squared over r So, if you think about the math, this is just like 1/2 minus one, and so that's going to R, so we plug that in, and now we can calculate the total energy. We plug that into here, and then we also found theĮlectrical potential energy is: negative Ke squared over We found the kinetic energy over here, 1/2 Ke squared over r, so So this would be theĮlectrical potential energy.
#DISCRETE CHARGE OF ELECTRON PLUS#
To the kinetic energy, plus the potential energy. With that electron, the total energy would be equal to: so, E-total is equal And to find the total energyĪssociated with that electron, the total energy associated Alright, so now we have theĮlectrical potential energy, and we have the kinetic energy. This negative sign in, because it's actually important. So we get: negative Ke squared over r So we define theĮlectrical potential energy equal to zero at infinity. Leave the negative sign in, and that's a consequence of how we define electrical potential energy. "q1", again, "q1" is theĬharge on the proton, so that's positive "e", and "q2" is the charge on the electron, so that's negative "e", negative "e", divided by "r". That's the charge of the proton, times the charge of the electron, divided by the distance between them. So the electrical potential energy is equal to: "K", our same "K", times "q1", so the charge of one. And that potential energy is given by this equation in physics. So the potential energy of that electron. So we know the kinetic energy is equal to: 1/2 Ke squared over r Alright, so we will comeīack to the kinetic energy. Here, we have mv squared, so if we multiply both sides by 1/2, right, multiply both sides by 1/2, now we have an expression for the kinetic energy of the electron. Our goal was to try to find the expression for the kinetic energy, And you can see, we'reĪlmost to what we want. if we only care about the magnitude, on the left side, we get: Ke squared over r is equal to Magnitude of the electric force because we already know the direction is always going to be towards the center, and therefore, we only care. So, centripetal acceleration is equal to "v squared" over "r". The charge on the electron, divided by "r squared", is equal to the mass of the electron times the centripetal acceleration. Is the same magnitude as the charge on the proton,īut it's a negative value. Write that in here, "q1", "q1" is the charge on a proton, which we know is elemental charge, so it would be positive "e". The electric force is a centripetal force, keeping it in circular motion, so we can say this is the We're talking about the electron here, so the mass of the electron times the acceleration of the electron. We know that Newton's Second Law: force is equal to the mass It's the charge on the proton, times "q2", charge on the electron, divided by "r squared", where "r" is the distanceīetween our two charges. Given by Coulomb's Law, the magnitude of the electric force is equal to K, which is a constant, "q1", which is, let's say We're gonna use it to come up with the kinetic energy for that electron. And, once again, we talkedĪbout the magnitude of this electric force in an earlier video, and we need it for this video, too. This is a centripetal force, the force that's holding that electron in a circular orbitĪround the nucleus here. There's an electric force,Īlright, so this electron is pulled to the nucleus,
So we know the electron isĪlso attracted to the nucleus. We're doing the Bohr model, there's a certain radius associated with where that electron is. We have one proton in the nucleus for a hydrogen atom, using the Bohr model, and we know, we know, that if The negative charge, the velocity vector, it'dīe tangent at this point. Going this way around, if it's orbiting our nucleus, so this is our electron, Alright, so we need to talk about energy, and first, we're going to try to find the kinetic energy of the electron, and we know that kineticĮnergy is equal to: 1/2 mv squared, where "m" is the mass of the electron, and "v" is the velocity. Of derivation using physics, so you can jump ahead to the next video to see what we come up with in this video, to see how it's applied. And so we're gonna be talkingĪbout energy in this video, and once again, there's a lot If we continue with our Bohr model, the next thing we have to talk about are the different energy levels.
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