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Question

What is the temperature at which the rms speed of helium atoms is 1000 m/s? (Atomic mass of He = 4 u, k_B = 1.38 × 10⁻²³ J K⁻¹)

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Explanation

**Partial pressure concept** for mixture of non-reacting gases, total pressure sum of partials, each gas behaves independently, kinetic theory still holds with effective n = Σ n_i, mean free path depends on total n and cross-sections, mixture properties weighted by mole tions. v_rms = √((3k_B T)/(m)), m = 4 × 10⁻³⁶.02 × 10²³ = 6.64 × 10⁻²⁷ kg.1000² = 3 × 1.38 × 10⁻²/³ × T6.64 × 10⁻²⁷, T = 10⁶ × 6.64 × 10⁻²⁷/⁴.14 × 10⁻²/³ ≈ 1604 K . Substituting values gives 1604 K, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law

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