Use the following to answer the question below:

-The probability that an energy state in magnesium 0.05 eV above the Fermi energy is occupied at T = 300 K is
A)1.26%
B)2.52%
C)3.78%
D)12.6%
E)14.5%

Question

Use the following to answer the question below:

-The probability that an energy state in magnesium 0.05 eV above the Fermi energy is occupied at T = 300 K is
A)1.26% 
B)2.52% 
C)3.78% 
D)12.6% 
E)14.5%

Quizplus · Accepted Answer

The probability that an energy state with energy E above the Fermi energy is occupied at T = 300 K is given by the Fermi-Dirac distribution function: P(E) = 1 / (1 + exp((E - Ef)/(kT))), where Ef is the Fermi energy, k is the Boltzmann constant and T is the temperature. For magnesium, the Fermi energy is 4.36 eV and the energy of interest is 4.41 eV (0.05 eV above Ef). Plugging in these values and using kT = 0.026 eV (at T = 300 K), we get P(E) = 0.126 or 12.6%. Therefore, the best choice is (D).

Use the Following to Answer the Question Below