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A container holds a mixture of two non-reacting ideal gases A (diatomic) and B (monoatomic) at constant temperature. The ratio of molar masses M_A: M_B = 4: 1. What is the ratio of their rms speeds v_A: v_B?

1. 1: 1
2. 1: 2
3. 1: sqrt(2)
4. sqrt(2): 1

Correct answer: 1: 2

Solution

The rms speed of a gas molecule is v_rms = sqrt(3RT/M), where M is the molar mass. Since both gases are at the same temperature T, the ratio v_A/v_B = sqrt(M_B/M_A) = sqrt(1/4) = 1/2. Therefore v_A: v_B = 1: 2.

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