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Question

The root mean square(rms) of molecules of nitrogen gas is v at a certain temperature. When the temperature is doubled, the molecules dissociate into individual atoms. The new rms speed of the atom is:

A
2v
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B
2v
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C
v
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D
4v
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Solution

The correct option is B 2v
We know that RMS velocity is given by: v=3RTM
According to the conditions given:
The final temperature (T2) and final molar mass (M2) is,
T2=2T,M2=M2
v2=  3R×2TM2=2v
Hence, the correct Option is (b).

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