Question

The rms speed of oxygen is $v$ at a particular temperature. If the temperature is doubled and oxygen molecules dissociates into oxygen atoms; the rms speed becomes:

• A. $v$
• B. $\sqrt{2v}$
• C. $2v$
• D. $4v$

Answer 1

Answer: (C)

$2v$

As the rms speed is given by
$V_{rms}=\sqrt{\frac{3RT}{M}}$
$\Rightarrow V_{rms}\propto \sqrt{\frac{T}{M}}$
When temperature is doubled and molecules dissociates into atoms, then
$\frac{V_{rm{s}_1}}{V_{rm{s}_2}}=\frac{\sqrt{\frac{T}{M}}}{\sqrt{\frac{2T}{M/2}}}=\frac{\sqrt{\frac{T}{M}}}{\sqrt{\frac{4T}{M}}}$
$=\frac{\sqrt{T}}{\sqrt{4T}}=\frac{1}{2}$
If $V_{rm{s}_1}$ is V, then $V_{rm{s}_2}$ will be 2V.