Use the following to answer the question below:

-The probability that an energy state in magnesium 0.2 eV above the Fermi energy is occupied at T = 300 K is
A)0.0365%
B)0.0404%
C)0.0438%
D)0.0457%
E)0.0496%

Question

Use the following to answer the question below:

-The probability that an energy state in magnesium 0.2 eV above the Fermi energy is occupied at T = 300 K is
A)0.0365% 
B)0.0404% 
C)0.0438% 
D)0.0457% 
E)0.0496%

Quizplus · Accepted Answer

Using the Fermi-Dirac distribution: 
f(E) = 1/[exp((E-E_F)/(k_B*T))+1]
where E_F is the Fermi energy, k_B is the Boltzmann constant, and T is the temperature. 
We are given that the energy state is 0.2 eV above the Fermi energy, so E - E_F = 0.2 eV. 
At T = 300 K, plugging in the values, we get: 
f(E) = 1/[exp(0.2 eV/(k_B*300 K))+1] = 0.0438
Therefore, the probability that the energy state is occupied is 0.0438 or 4.38%, which corresponds to choice C.

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