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The Maxwell distribution of speeds of two different gases of molar masses $M_{1}$ and $M_{2}$ at 300 K is given below:

The value of $4 \frac{M_{1}}{M_{2}}$ is_______. (Use R = 8.3 $J m o l^{- 1} K^{- 1}$ )

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answer is 9.

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Detailed Solution

$U_{m p} = \sqrt{\frac{2 R T}{M}}$

$\Rightarrow \sqrt{\frac{2 \times 8.3 \times 300}{M_{1} \times 10^{- 3}}} = 500$

$& \sqrt{\frac{2 \times 8.3 \times 300}{M_{2} \times 10^{- 3}}} = 750$

$\Rightarrow \frac{M_{1}}{M_{2}} = \frac{9}{4}$

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