For an assembly of molecules (molar mass =M) at temperature T, the standard deviation of Maxweller's speed is approximately

(a) 0.7 √(RT/M). Explanation: σ = √(⟨v²⟩ − ⟨v⟩²) = √((3 − 8/π)RT/M) = 0.67√(RT/M) ≈ 0.7√(RT/M) (a).

Q99 · CSIR-NET Chemistry, June 2011

Paper: CSIR-NET June 2011 · Subject: Physical Chemistry · Chapter: Atomic and Molecular Term Symbol · Topic: Atomic And Molecular Term Symbols – General · Marks: 2 · Difficulty: Medium

For an assembly of molecules (molar mass $=\mathrm{M}$ ) at temperature T , the standard deviation of Maxweller's speed is approximately

(a)$0.7 \sqrt{\frac{\mathrm{RT}}{\mathrm{M}}}$

(b)$1.4 \sqrt{\frac{\mathrm{RT}}{\mathrm{M}}}$

(c)$0.7 \sqrt{\frac{\mathrm{M}}{\mathrm{RT}}}$

(d)$1.4 \sqrt{\frac{\mathrm{M}}{\mathrm{RT}}}$

Answer

Answer: A ✓ checked by 4AB · confidence high

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

Explanation

σ = √(⟨v²⟩ − ⟨v⟩²) = √((3 − 8/π)RT/M) = 0.67√(RT/M) ≈ 0.7√(RT/M) (a).

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