Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: If the average kinetic energy of \(H_2\) and \(O_2\) molecules, kept in two different sized containers are same, then their temperatures will be same.

Reason R: The r.m.s. speed of \(H_2\) and \(O_2\) molecules are same at same temperature.

Choose the correct answer from the options given below

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