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Question

If the rms speed of nitrogen molecules is 490 ms1 at 273K, find the rms speed of hydrogen molecules at the same temperature -


A

1580 m/s

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B

1830 m/s

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C

1700 m/s

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D

2150 m/s

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Solution

The correct option is B

1830 m/s


The molecular weight of nitrogen (N2) is 28 g mol1 and that of hydrogen (H2) is 2 g mol1. Let m1 and m2 be the masses, v1 and v2 be the rms speeds of a nitrogen molecule and a hydrogen molecule respectively. Then m1=14m2. Since the kinetic energies of the hydrogen and nitrogen molecules will be the same at the same temperature -

12m1v21=12m2v22

or, v2=v1m1m2=490 m s1×14=1830 m s1.


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