1. The problem statement, all variables and given/known data Show that the fraction of electrons within kT of the fermi level is equal to 3kT/2Ef, if D(E) = E^1/2. 2. Relevant equations f(E) = 1 / ( exp(E-Ef)/kT + 1 ) fermi distribution N = integral from 0 to inf of D(E)f(E)dE = total no. of electrons 3. The attempt at a solution I'm really lost with this problem. I'm not even sure if I have to solve it at T = 0, in which case I tried to calculate n = integral from Ef - kT to Ef of D(E)f(E)dE over N = integral from 0 to Ef of D(E)f(E)dE with f(E) = 1, OR at a temperature T which is finite such that now I calculate n = integral from Ef - kT to Ef + kT of D(E)f(E)dE over N as defined in "relevant equations" above. In the first case I get a horrible algebraic expression which does not simplify to what I'm supposed to get and in the second case I get integrals I don't know how to evaluate and can't even calculate using mathcad. Any hints would be highly appreciated. Thanks!