Use the following to answer the question below:

-At what energy is the Fermi factor equal to 0.1 for magnesium at T = 300 K?
A)7.08 eV
B)7.17 eV
C)7.05 eV
D)7.02 eV
E)7.18 eV

Question

Use the following to answer the question below:

-At what energy is the Fermi factor equal to 0.1 for magnesium at T = 300 K?
A)7.08 eV 
B)7.17 eV 
C)7.05 eV 
D)7.02 eV 
E)7.18 eV

Quizplus · Accepted Answer

The Fermi-Dirac distribution function can be expressed as: f(E) = 1/(1 + exp[(E-E_F)/(k_BT)])
where E_F is the Fermi energy, k_B is the Boltzmann constant, and T is the temperature.
For the Fermi factor to be equal to 0.1, we have: f(E) = 0.1, which leads to: E - E_F = -2.303k_BT ln(1/0.1) = 2.303k_BT ln(10) = 2.303(8.617x10^-5 J/K)(300 K) ln(10) = 0.587 eV. 
Substituting E_F = 7.68 eV (the Fermi energy for magnesium), we get: E = E_F + 0.587 eV = 8.267 eV. 
Therefore, the closest answer choice is B) 7.17 eV.

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