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Root Mean Square Velocity

The root mean...

Question

The root mean square speed 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

\sqrt{2} v

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B

2 v

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C

v

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D

4 v

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Solution

The correct option is B $2 v$
We know that RMS velocity is given by: $v = \sqrt{\frac{3 R T}{M}}$
According to the conditions given:
The final temperature $(T_{2})$ and final molar mass $(M_{2})$ is,

$T_{2} = 2 T, M_{2} = \frac{M}{2}$

$v_{2} = \sqrt{\frac{3 R \times 2 T}{\frac{M}{2}}} = 2 v$

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Root Mean Square Velocity

Standard XII Chemistry

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