N non-interacting molecules are distributed among three non-degenerate energy levels ε₀=0, ε₁=1.38×10²¹ J and ε₂ = 2.76×10⁻²¹ J, at 100 K. If the average total energy of the system at this temperature is 1.38×10⁻¹⁸ J, the number of molecules in the system is:

N non-interacting molecules are distributed among three non-degenerate energy levels ε₀=0, ε₁=1.38×10²¹ J and… · ABC26PH0547

Subject: Physical Chemistry · Chapter: Statistical Thermodynamics · Topic: Statistical Thermodynamics – General · Exam: GATE 2005-2021 · Marks: 2 · Difficulty: Medium

N non-interacting molecules are distributed among three non-degenerate energy levels $\varepsilon_{0}=0, \varepsilon_{1}=1.38\times10^{21}\,\mathrm{J}$ and $\varepsilon_{2} \; = \; 2.76\times10^{-21}\,\mathrm{J}$, at 100 K. If the average total energy of the system at this temperature is $1.38\times10^{-18}\,\mathrm{J}$, the number of molecules in the system is:

(a)1000

(b)1503

(c)2354

(d)2987

Answer

Answer: C ✓ checked by 4AB · confidence high

The source book printed A; on checking, C is correct — see the explanation.

Book printed (a).

Explanation

ε₁/kT = 1: q = 1 + e⁻¹ + e⁻² = 1.503; ⟨ε⟩ = 1.38×10⁻²¹ × (e⁻¹ + 2e⁻²)/1.503 = 5.86×10⁻²² J; N = 1.38×10⁻¹⁸/5.86×10⁻²² ≈ 2354 (c).

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