Use the following to answer the question below:

-The probability that an energy state in copper 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 copper 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

To calculate the probability that an energy state in copper 0.2 eV above the Fermi energy is occupied at T = 300 K, we can use the Fermi-Dirac distribution function:
f(E) = 1 / [1 + exp((E - Ef)/(kT))]
where Ef is the Fermi energy, k is the Boltzmann constant, and T is the temperature. 
Since we want to find the probability of occupation for an energy state 0.2 eV above the Fermi energy, we can plug in (Ef + 0.2) for E in the above equation. 
Using the values given for copper at T = 300 K (Ef = 7 eV and k = 8.617 x 10^-5 eV/K), we get:
f(Ef + 0.2) = 1 / [1 + exp((0.2)/(kT))] = 0.0438%
Therefore, the best choice is C with a probability of 0.0438%.

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