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AP EAMCET · PHYSICS · Kinetic Theory of Gases

The absolute temperature at which the rms speed of a hydrogen molecule is equal to its escape speed from the moon's surface is (where, \(R\) is radius of moon is \(r, g\) is acceleration due to gravity on Moon's surface, \(m\) is mass of hydrogen molecules and \(k\) is Boltzmann constant)

  1. A \(\frac{m g R}{2 k}\)
  2. B \(\frac{2 m g R}{k}\)
  3. C \(\frac{3 m g R}{2 k}\)
  4. D \(\frac{2 m g R}{3 k}\)
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Answer & Solution

Correct Answer

(D) \(\frac{2 m g R}{3 k}\)

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Detailed explanation

\begin{aligned} & v_{\text {rms }}(\text { hydrogen })=\sqrt{\frac{3 R T}{M}}=\sqrt{\frac{3 k T}{m}} \\ & \text { and } v_{\text {escape }}(\text { moon })=\sqrt{2 g R} \\ & v_{\text {rms }}=v_{\text {escape }} \\ & \Rightarrow \quad \frac{3 k T}{m}=2 g R \Rightarrow T=\frac{2 m…