Free-Electron Theory of Metals: What Is the Occupancy Probability at an Energy

Multiple Choice

Free-electron theory of metals: What is the occupancy probability at an energy of 12.00 eV for a material with a Fermi energy (level) of 11.63 eV at a temperature of 500 K? (m_el = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s, Boltzmann constant = 1.38 × 10^-23, 1 eV = 1.60 × 10^-19 J)

A) 0.00030%
B) 0.019%
C) 2.0%
D) 6.0%
E) 12%