density of states, fermi energy

1. The problem statement, all variables and given/known data
Consider an electron gas with a density of states given by D(e) = ae2. Here a is a constant. The Fermi energy is e_F.
a) We first consider the system at zero temperature. Compute the total number of electrons N and the groundstate
energy E. Show that the average energy per electron in the groundstate is given by (3/4)e_F.

2. Relevant equations
many available expressions for the number of electrons but dont know which one to use.

i.e N(E)= V/3?²(2mE/hbar²)^3/2

lacking expressions for energy
3. The attempt at a solution

Source: http://www.physicsforums.com/showthread.php?t=562719&goto=newpost

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