Answer
At E = 6.75 eV,
$N_0=1.68\times 10^{28} m^{-3}.eV^{-1}$
Work Step by Step
At E = 6.75 eV,
$N_0 = \frac{6.81\times 10^{27} m^{-3}.eV^{-3/2}(6.75 eV)^{1/2} }{[e^{6.75 eV - 7.00eV/(8.62 \times 10^{-5} eV/K)(1000K)} + 1]}$
$N_0=1.68\times 10^{28} m^{-3}.eV^{-1}$