For free electrons in a metal, the depth of a potential well can be determined by observing that the work function is the energy required to remove an electron at the top of the occupied states from the metal; an electron in this state has the Fermi energy.
Assuming each atom provides one free electron to the gas, find the depth of the well for a free electron in gold (work function = 4.8 eV)
The Attempt at a Solution
I'm assuming that the answer will be just the fermi energy plus the work function, but I can't seem to get the right answer when plugging everything in.
For N/V, I used (Avogadro # x Density of gold) / (molar mass of gold) , and got 3.89 x 10^9 electrons / cubic meter
The answer should be on the order of 1 ev, but I can't seem to get this. The m here refers to the mass of a single electron, correct? But using that, I just don't get the right orders of magnitude. (I get about 5 x 10^6).