Question Bank MCQ • 2 Marks Section 5: Thermodynamics & Statistical Physics Bose-Einstein and Fermi-Dirac statistics

QB_PH_129: Bose-Einstein and Fermi-Dirac statistics

Question Statement

The Fermi energy $E_F$ of a 3D non-interacting electron gas depends on particle density $n$ as:
(A) n^{2/3}
(B) n^{1/3}
(C) n^{3/2}
(D) n^2
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $E_F = \frac{\hbar^2}{2m}(3\pi^2 n)^{2/3} \propto n^{2/3}$.
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