Two identical vessels contain two different ideal gases at the same...

Two identical vessels contain two different ideal gases at the same temperature. If the average speed of gas molecules in the first vessel is equal to the most probable speed of molecules in the second vessel, then the ratio of the mass of gas molecules in the first vessel to that in the second vessel is

Options

A $\dfrac{4}{\pi}$
B $\dfrac{8}{\pi}$
C $\dfrac{2}{\pi}$
D $\dfrac{\pi}{2}$

Correct answer

A. $\dfrac{4}{\pi}$

Step-by-step solution

{v}_{avg} = \sqrt{\dfrac{8RT}{\pi M1}}

{v}_{mp} = \sqrt{\dfrac{2RT}{M2}}

\dfrac{8}{{M}_{1}\pi} = \dfrac{2}{M2}

\dfrac{M1}{M2} = \dfrac{4}{\pi}

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