At what temperature the rms velocity of helium molecules will be equal to that of hydrogen molecules at NTP?

844K

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64 K

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273

^{0}

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273K

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Solution

The correct option is B 273 $^{0}$ C
$C_{r m s} = \sqrt{\frac{3 R T}{M}} \sqrt{\frac{3 R T_{h e l i u m}}{M_{h e l i u m}}} = \sqrt{\frac{3 R T_{h y d r o g e n}}{M_{h y d r o g e n}}} \sqrt{\frac{273}{2}} = \sqrt{\frac{T_{h e l i u m}}{4}} T_{h e l i u m} = 546 K = 273^{0} C$

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