GATE 2020 PH – Question 21
Choose the correct relation between Fermi energy $E_F$ and chemical potential $\mu$ of a metal.
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Correct answer: (A) $\mu=E_F$ only at 0 K.
Explanation
The Fermi energy is conventionally the zero-temperature chemical potential: $\mu(0)=E_F$. For an ordinary three-dimensional metallic electron gas at small nonzero T, $\mu(T)\simeq E_F[1-\pi^2(k_BT/E_F)^2/12]$, so it generally departs from the zero-temperature value. The intended relation is A.