First slide

Rms speed

Question

The rms speed of oxygen is v at a particular temperature. If the temperature is doubled and oxygen molecules dissociate into oxygen atoms, the rms speed becomes [WB JEE 2015]

Moderate

A

v
B

$\sqrt{2} v$
C

2v
D

4v

Solution

The rms speed is given by
$v_{rms} = \sqrt{\frac{3 R T}{M}}$
$\Rightarrow v_{rms} \propto \sqrt{\frac{T}{M}}$
When temperature is doubled and molecules dissociate into atoms, then
$\frac{{(v_{rms})}_{1}}{{(v_{rms})}_{2}} = \frac{\sqrt{\frac{T}{M}}}{\sqrt{\frac{2 T}{M / 2}}} = \frac{\sqrt{\frac{T}{M}}}{\sqrt{\frac{4 T}{M}}} = \frac{\sqrt{T}}{\sqrt{4 T}} = \frac{1}{2}$
If ${(v_{r m s})}_{1}$ is v, then ${(v_{r m s})}_{2}$ will be 2v.

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