00:01
All right, so let's say the fermi energy for a particular material is 5 .5 electron volts.
00:07
Part a of this question is to find the probability of an electron occupying of an energy of 5 .8 electron volts, given that the temperature is 300 kelvin.
00:23
So the probability, we'll just call this n or something like this, is our fermi function.
00:30
This is 1 over e to the beta e minus ef plus 1.
00:40
So if we plug in the numbers for this, this will be the exponential.
00:46
And let's actually, sorry, let's write boltsman's constant real quick.
00:49
So 1 .3 .8.
00:52
This is about 8 .625 times 10 to the negative 5th electron volts per kelvin.
01:01
So this will be the exponential let me write it this way of the difference between the fermi energy and the energy so 0 .3 electron volts over 8 .625 times 10 to the negative 5th electron volts per kelvin times 300 kelvin and then plus one and then the reciprocal of that so if you do that plus one take the reciprocal this is like 9 .22 times 10 to the negative 6th and then part b we want to do the same thing but at the temperature of 700 kelvin so then we'll do 8 .625 so the negative 5th times 700 reciprocal times 0 .3 exponential of that plus 1 take the reciprocal now it's going to be about 6 .9 times 10 to the negative 3rd and then the term the temperature at which there is a 2 % probability that a state 0 .25ev below the fermi level will be empty.
02:17
So the probability that a state will be empty is like one minus the probability that it will be full.
02:25
So what you can do is write it as like one minus one over e to the beta.
02:31
We'll just call this delta e like the difference between the fermi energy and the energy in question.
02:37
So if you write this out, this is like e to the beta delta e plus one over e to the beta delta e plus one minus one over this.
02:51
So it's really basically this is what we get in up with...