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

QB_PH_133: Bose-Einstein and Fermi-Dirac statistics

Question Statement

In a 3D non-interacting Bose gas, the critical condensation temperature $T_c$ scales with number density $n$ and mass $m$ as:
(A) n^{2/3} / m
(B) n^{1/3} / m
(C) n / m^2
(D) n^{3/2} m
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $T_c = \frac{2\pi \hbar^2}{m k_B}\left(\frac{n}{\zeta(3/2)}\right)^{2/3} \propto \frac{n^{2/3}}{m}$.
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