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Q.

At what temperature will hydrogen molecules have same root mean square velocity as helium atoms at  291 K?

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answer is 145.5.

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Detailed Solution

Mol. wt. of H2=2gmol− mol. wt. of He= at. wt. of            He=4.0gmol−;T=291K.Both He and H2 have same root mean square speed,   u For He, U=3RTM1/2=3R×291K4gmol−1/2…(1)For  H2′ U=(3RTM)1/2=(3R×T2.0gmol−)1/2−(2)∴ 291K41/2=T21/2Squaring both sides, we get291K4=T2;T=291K×24=145.5K
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