A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at $300\ K.$ The ratio of the average rotational kinetic energy per $O_2$ molecule to that per $N_2$ molecule is
A$1 : 1$
B$1 : 2$
C$2 : 1$
D
Depends on the moments of inertia of the two molecules
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A$1 : 1$
a Average kinetic energy per molecule per degree of freedom $=\frac{1}{2} k T$ since, both the gases are diatomic and at same temperature $(300 \mathrm{K}),$ both will have the same number of rotational degree of freedom i.e. two. Therefore, both the gases will have the same average rotational kinetic energy per molecule
$=2 \times \frac{1}{2} k T o r k T$
$\Rightarrow$ Thus, ratio will be $1: 1$
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