The temperature at which oxygen molecules have the same root mean square speed as helium atoms have at $300 K$ is:
(Atomic masses; $H e = 4 u, O = 16 u)$

1200 K

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600 K

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300 K

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2400 K

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Solution

The correct option is D $2400 K$
Given Atomic masses : $H e = 4 u$ , $O = 16 u$
$(V_{r m s}) O_{2} = (V_{r m s}) H e \sqrt{(\frac{3 R T_{1}}{M_{1}})} = \sqrt{(\frac{3 R T_{2}}{M_{2}})} \frac{T_{1}}{M_{1}} = \frac{T_{2}}{M_{2}} \frac{T_{1}}{32} = \frac{300}{4} T_{1} = 300 \times \frac{32}{4} = 2400 K$

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H e = 4 u, O = 16 u)

300 K

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At what temperature will oxygen molecules have the same root mean square speed as hydrogen Molecules at $200 K$ ?

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