In Si the effective density of states in the conduction band is Nc=3.2×10¹⁹ cm⁻³ at room temperature, and that of the valence band is Pv=1.8×10¹⁹ cm⁻³. The band gap of Si is Eg=1.12 eV. Mobilities of electrons and holes in high purity Si are µe=1500 cm²/(V*sec) and µh=500 cm²/(V*sec), respectively.
Calculate the intrinsic carrier density of Si at room temperature.