Given below are two statements: one is labelled as Assertion A and...

The average kinetic energy of a gas molecule is directly proportional to its absolute temperature and is given by $E = \dfrac{f}{2} k_B T$, where $f$ is the degree of freedom. Since both $H_2$ and $O_2$ are diatomic gases, they have the same degrees of freedom ($f=5$). Therefore, if their average kinetic energies are the same, their temperatures must be the same. Thus, Assertion A is true.

The root mean square (r.m.s.) speed of a gas molecule is given by $v_{rms} = \sqrt{\dfrac{3RT}{M}}$. Since the molar mass $M$ of $H_2$ ($2 \text{ g/mol}$) is different from that of $O_2$ ($32 \text{ g/mol}$), their r.m.s. speeds will be different even at the same temperature. Thus, Reason R is false.

Therefore, A is true but R is false.

Answer: A is true but R is false