00:01
So this question gives us the temperature of conduction electron in silver at 800 kelvin.
00:06
It gives us the fermi energy of silver, which is 5 .48 electron volts.
00:11
And then we'll also give them the probability of finding an electron in that state, which is 0 .950.
00:17
I've denoted that as f of e here.
00:20
And we're asked to work out what the energy e is.
00:24
So to start, we can define the fermi function, f of e, to be equal to 1 over, we have 1 plus e to the e being our energy, minus the fermi energy ef, and that is all over k, the boltzman constant times by the temperature t.
00:50
And this function simply represents the probability of finding an electron in the state e for a metal with temperature t.
01:00
So we need to rearrange to find the e.
01:03
So what we will first do is we will multiply this denominator up to the other side and take f of e down to the other side.
01:11
So that will look like, so we have our left -hand side 1 plus e to the e minus e f all over kt is equal to 1 over f of e.
01:32
So the plan from here is where we need to take the 1 over to the other side and then take the natural logarithm of both sides to remove this exponential dependence on the energy so that we can solve for it...