Physics - Heat & Thermo Question with Solution | TestHub

RMS speed of $O_2$ gas is $v_{\mathrm{rms}}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3RT}{32}}$ and most probable speed of $O_2$ gas is $v_{\mathrm{most} \mathrm{probable}}=\sqrt{\frac{2RT}{M}}=\sqrt{\frac{2RT}{32}}$.

Here temperature is same.

Thus, $\frac{v_{\mathrm{rms}}}{v_{\mathrm{most} \mathrm{probable}}}=\frac{\sqrt{{\displaystyle \frac{3RT}{32}}}}{\sqrt{{\displaystyle \frac{2RT}{32}}}}=\sqrt{\frac{3}{2}}$

Hence, $v_{\mathrm{rms}}=\sqrt{\frac{3}{2}}{v}_{\mathrm{p}}$