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Question

# If the rms speed of nitrogen molecules is 490 msâˆ’1 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 mol−1 and that of hydrogen (H2) is 2 g mol−1. 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=v1√m1m2=490 m s−1×√14=1830 m s−1.

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