In a silicon semiconductor at room temperature, the intrinsic carrier concentration is \( 1.5 \times 10^{16} \, \text{m}^{-3} \). Calculate the energy band gap of the silicon if the intrinsic carrier concentration is given by:
\[
n_i = \sqrt{N_c N_v} e^{-E_g / 2kT}
\]
Where:
- \( N_c = 2.8 \times 10^{25} \, \text{m}^{-3} \) is the effective density of states in the conduction band,
- \( N_v = 1.04 \times 10^{25} \, \text{m}^{-3} \) is the effective density of states in the valence band,
- \( k = 1.38 \times 10^{-23} \, \text{J/K} \) is the Boltzmann constant,
- \( T = 300 \, \text{K} \) is the temperature.