Gallium Arsenide is a semiconductor with conduction band effective density of states of Nc = 4.7 × 1017 cm−3 , valence band effective density of states Nv = 7 × 1018 cm−3 , and energy gap Eg = 1.43 eV. 1a. Calculate the intrinsic carrier concentration ni in GaAs at 300 K. 1b. What is the length of one side of a cube of pure (intrinsic) GaAs that contains, on average, one electron-hole pair at 300 K. 1c. What is the difference in energy between the Fermi level EF and the valence band maximum Ev in intrinsic GaAs at 300 K? Your answer should be precise to within ±10 meV.