Question

What is the ratio of mean speed of an $O_2$ molecule to the rms speed of an $O_2$ molecule at the same $T$?

• A. ${\left(3\pi /7\right)}^{1/2}$
• B. ${\left(8/3\pi \right)}^{1/2}$
• C. ${\left(3\pi \right)}^{1/2}$
• D. ${\left(4\pi /9\right)}^{1/2}$

Answer 1

The correct option is B ${\left(8/3\pi \right)}^{1/2}$

The ratio of mean speed of an $O_2$ molecule to the rms speed of an $O_2$ molecule at the same T is $\frac{v}{u}=\sqrt{\frac{8}{3\pi }}$.
Mean speed $v=\sqrt{\frac{8RT}{\pi M}}$

RMS speed $u=\sqrt{\frac{3RT}{M}}$

$\frac{v}{u}=\frac{\sqrt{\frac{8RT}{\pi M}}}{\sqrt{\frac{3RT}{M}}}$

$\frac{v}{u}=\sqrt{\frac{8}{3\pi }}$