Answer
At $E=4.00eV$,
$N_0 = 1.36 \times 10^{28} m^{-3}.eV^{-1}$
Work Step by Step
The main formula is
$N_0(E) = N(E) P(E)$
$N_0(E) = CE^{1/2} [e^{E_1 - E_F/kT} + 1]^{-1}$
Where C is
$C = \frac{8\sqrt 2 \pi (9.109\times 10^{-31} kg)^{3/2}}{(6.626\times 10^{-34} J.s)^3}$
$C = 1.062 \times 10^{56} kg^{3/2}/J^3.s^3$
It can also be written as:
$C = 6.81\times 10^{27} m^{-3}.eV^{-3/2}$
At $E=4.00 eV$,
$E_F $ for copper is 7.00 eV
$k = 8.62 \times 10^{-5} eV/K$
$T = 1000K$
$N_0(E) = \frac{6.81\times 10^{27} m^{-3}.eV^{-3/2}(4.00 eV)^{1/2} }{[e^{4.00 eV - 7.00eV/(8.62 \times 10^{-5} eV/K)(1000K)} + 1]}$
$N_0 = 1.36 \times 10^{28} m^{-3}.eV^{-1}$
