Question

The relation between root mean square speed $(v_{rms})$ and most probable speed ($v_p$) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be

• A. $v_{rms} = \sqrt {\frac 23}v_p$
• B. $v_{rms} = \sqrt {\frac 32}v_p$
• C. $v_{rms} = v_p$
• D. $v_{rms} = \sqrt {\frac 13}v_p$

Answer 1

Answer: (B)

$v_{rms} = \sqrt {\frac 32}v_p$

Answer 2

$v_{rms} = \sqrt {\frac {3RT}{M}}$
$v_p = \sqrt {\frac {2RT}{M}}$
⇒ $v_{rms} = \sqrt {\frac 32}v_p$

So, the correct option is (B): $v_{rms} = \sqrt {\frac 32}v_p$