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  4. At 300 K, the rms speed of oxygen molecules is √(α+5/α) times to that of its average speed in the gas. Then, the value of α will be (used π=(22/7) )

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Q. At $300 K$, the rms speed of oxygen molecules is $\sqrt{\frac{\alpha+5}{\alpha}}$ times to that of its average speed in the gas. Then, the value of $\alpha$ will be (used $\pi=\frac{22}{7}$ )

JEE MainJEE Main 2023Kinetic Theory

Solution:

$ \sqrt{\frac{3 RT }{ M }}=\sqrt{\frac{\alpha+5}{\alpha}} \sqrt{\frac{8}{\pi} \frac{ RT }{ M }} $
$3=\frac{\alpha+5}{\alpha} \frac{8}{\pi} $
$ \alpha=28$