00:01
In this problem, we're going to talk about relativistic energy.
00:03
So remember that the energy of a massive relativistic particle is equal to mc squared times gamma, where gamma is 1 over the square root of 1 minus v squared over c squared.
00:19
The rest energy is 0 is equal to mc squared.
00:24
And the kinetic energy is the total energy minus the rest energy, and this is mc squared times gamma minus 1.
00:36
And our goal in our exercise is to calculate what is the velocity of an electron that is accelerated through a potential difference, v, that is equal to 20 times 10 to 6 volts.
00:55
So the first thing we need to remember is that the kinetic energy of a charged particle that is accelerated through a potential v is equal to the magnitude of the charge of a particle, in this case, it's e times the potential v.
01:19
So in our case, this is 1 .6 times 10 to the minus 19 quillums.
01:25
This is the charge of the electron times v, which is 20 times 10 to the 6 volts.
01:32
So the kinetic energy is equal to 3 .2 times 10 to the minus 12 joules.
01:46
This is the kinetic energy of the electron.
01:51
And now with the kinetic energy, we can find the value of the velocity...