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JEE Advanced levelSingle correct optionDifficulty 3 of 3ig200

At $300 K$ a gas sample has a Maxwell distribution with most probable speed $u_{0}$ . The temperature at which the fraction of molecules having speed $u_{0}$ becomes maximum in the distribution of a gas with double the molar mass is

A $600 K$
B $150 K$
C $300 K$
D $1200 K$

Answer: A

The fraction at speed

u_{0}

is a maximum when

u_{0}

is the most probable speed of the heavier gas:

2 R T^{'} / (2 M) = 2 R (300) / M

, so

T^{'} /2 = 300

,

T^{'} = 600 K

.

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