The r.m.s. speed of oxygen molecule in a vessel at a particular temperature is where is the average speed of the molecule. The value of will be: (Take ) [2023]

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Solution

Q.
The r.m.s. speed of oxygen molecule in a vessel at a particular temperature is ${(1 + \frac{5}{x})}^{1 / 2} v,$ where $v$ is the average speed of the molecule. The value of $x$ will be: (Take $π = \frac{22}{7}$ ) [2023]

1 28

2 27

3 8

4 4

Ans.
(1)

$\sqrt{\frac{3 R T}{M}} = {(1 + \frac{5}{x})}^{\frac{1}{2}} \sqrt{\frac{8 R T}{π M}}$

$\Rightarrow \frac{3 \times 22}{7 \times 8} = 1 + \frac{5}{x} \Rightarrow x = 28$

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