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

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

Answer 1

Answer: (C)

$2v$

Answer 2

As the rms speed is given by
$v_{ ms }=\sqrt{\frac{3 R T}{M}}$
$\Rightarrow v_{ ms } \propto \sqrt{\frac{T}{M}}$
When temperature is doubled and molecules dissociates 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 $v_{ rms _{1}}$ is $V$, then $V_{ rms _{2}}$ will be $2 v$.