Q 11-12-062JEE MainJEE Main 2023 (29 Jan, Shift 2)Medium
At $300\ \text{K}$, the rms speed of oxygen molecules is $\sqrt{\dfrac{\alpha+5}{\alpha}}$ times to that of its average speed in the gas. Then, the value of $\alpha$ will be (use $\pi=\frac{22}{7}$)
Answer: (B) 28
$$\frac{v_{rms}}{v_{avg}}=\sqrt{\frac{3RT/M}{8RT/\pi M}}=\sqrt{\frac{3\pi}{8}}=\sqrt{\frac{3\times22}{56}}=\sqrt{\frac{33}{28}}$$
Comparing with $\sqrt{\dfrac{\alpha+5}{\alpha}}$ gives $\alpha=28$.
Solution by Sreeraj P, M.Sc Physics