At 300 K, the rms speed of oxygen molecules is times to that of its average speed in the gas. Then, the value of will be (use ) [2023]

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Solution

Q.
At 300 K, the rms speed of oxygen molecules is $\sqrt{\frac{α + 5}{α}}$ times to that of its average speed in the gas. Then, the value of $α$ will be (use $π = \frac{22}{7}$ ) [2023]

1 32

2 28

3 24

4 27

Ans.
(2)

$\sqrt{\frac{3 R T}{M}} = \sqrt{\frac{α + 5}{α}} \sqrt{\frac{8}{π} \frac{R T}{M}}$

$3 = \frac{α + 5}{α} \frac{8}{π} \Rightarrow α = 28$

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