The ElectronVolt

Hey guys. In this video we're going to talk about something called an electron volt, let's get to it. Suppose we had two plates of equal and opposite charge, one had a charge plus q, when a charge negative q and they were separated such that the potential difference was 1 volt, okay? Just look at the figure above me, if we have an electron moving from one plate to the other, right? It would move from the negative to the positive plate just because the positive plate attracts the negative charges, what potential difference would have experienced? Well, the potential difference across the plates is 1 volt, so it experienced 1 volt of potential difference, the change in potential energy is then, well, Delta U, we know is q, Delta V, okay? q for an electron will say is 1e, 1 elementary charge, right? And the potential is 1 V. So, instead of actually writing, what e is in terms of the joules, sorry, in terms of coulombs, we'll leave it as is and then that change in potential energy is 1 e V. Note that as the electron moves from one place to another it's converting its potential energy into kinetic, it's expanding its stored energy so it can gain speed, this quantity of energy, this e, VI is known as an electron volt, okay? Since it's a unit of energy it can be easily related to a Joule, all we have to do to find it in joules is actually plug in that elementary charge in coulombs, right? 1.6 times 10 to the negative 19, and it's 1.6 times 10 to the negative 19 joules. Now, the convenience that comes from using an e VI is when you're dealing with charges like the elementary charge, charges that are very, very small your energy is always going to be small but your number could be not very small in electron volts, right? Like, if you had one electron going through two volts of potential difference, it would gain two e, V of kinetic energy, okay? q would stay the same but Delta V would now become 2 volts. So, gain 2 e, V of kinetic energy, if we were to write this in joules to be 3.2 times 10 to the negative 19 which is also a very, very small number. So, that's the convenience of an electron volt. Well, it's actually used the electron volt now, what is the speed of an electron with 150 e, V's of kinetic energy. So, it's kinetic energy is 150 e, V's before we can find the speed, we have to find this quantity of energy in joules, we can't use one-half m, v squared without a kinetic energy in the SI unit of Joule, so this is times 1 e, V under 1.6 times 10 to the negative 19 joules, that's just quick conversion, 2.4 times 10 to the negative 17 joules, okay? And this equals 1/2 m, v squared. So, rearranging this equation, if we multiply the 2 up divide the m over. V squared is 2 k over m taking the square root, that's 2 k over m Square rooted, which is 2 times 2.4 times 10 to the negative 17, the mass of an electron is 9.11 times 10 to the negative 31, okay? And that whole thing once, we take the square root 7.26 times 10 to the 6 meters per second, right? Quick and easy, that's the idea of an electron volt, it's just a unit of energy that makes representing certain things more convenient, alright? Thanks for watching.