Q102 · CSIR NET Chemistry, December 2014
Paper: CSIR NET December 2014 · Subject: Physical Chemistry · Chapter: Statistical Thermodynamics · Topic: Partition Functions · Marks: 2 · Difficulty: Medium
The low and high temperature limits of vibrational partition function are $(\theta = h\nu/k)$ :
(a)$e^{-\frac{\theta}{T}}$ and $\frac{T}{\theta}e^{-\frac{\theta}{T}}$
(b)$\mathrm{e}^{-\frac{\theta}{2 \mathrm{T}}}$ and $\frac{\mathrm{T}}{\theta} \mathrm{e}^{-\frac{\theta}{2 \mathrm{T}}}$
(c)$\mathrm{e}^{-\frac{\theta}{2 \mathrm{T}}}$ and $\frac{\mathrm{T}}{\theta} \mathrm{e}^{-\frac{\theta}{\mathrm{T}}}$
(d)$\mathrm{e}^{-\frac{\theta}{2 \mathrm{T}}}$ and $\frac{\theta}{\mathrm{T}} \mathrm{e}^{-\frac{\theta}{2 \mathrm{T}}}$
Answer
Answer: B ✓ checked by 4AB · confidence medium
The source book printed A; on checking, B is correct — see the explanation.
Explanation
With energy measured from the potential minimum, q_v = e^(−θ/2T)/(1 − e^(−θ/T)). At low T this tends to e^(−θ/2T); at high T it tends to (T/θ)e^(−θ/2T) (b).
Study loop for Statistical Thermodynamics