Question

The relation between root mean square speed $\left( v _{ rms }\right)$ and most probable speed $\left( v _{ p }\right)$ for the molar mass $M$ of oxygen gas molecule at the temperature of $300 \,K$ will be :-

• A. $v _{ rms }=\sqrt{\frac{2}{3}} v _{ p }$
• B. $v _{ rms }=\sqrt{\frac{3}{2}} v _{ p }$
• C. $v _{ rms }= v _{ p }$
• D. $v _{ rms }=\sqrt{\frac{1}{3}} v _{ p }$

Answer 1

Answer: (B)

$v _{ rms }=\sqrt{\frac{3 RT }{ M }} $
and $ v _{ mp }=\sqrt{\frac{2 RT }{ M }}$
Thus $v _{ rms }=\sqrt{\frac{3}{2}} v _{ mp }$