Question:

Which of the following statement(s) is (are) correct regarding the root mean square speed (Urms) and average translational kinetic energy (εav) of a molecule in a gas at equilibrium?

εav at a given temperature does not depend on its molecular mass

εav is doubled when its temperature is increased four times

Urms is doubled when its temperature is increased four times

Urms is inversely proportional to the square root of its molecular mass

Solution:

Correct option is A, C, and D.
εav at a given temperature does not depend on its molecular mass
The root mean square speed (Urms) and average translational kinetic energy (εav) has following relation with temperature and molecular mass
εav = (3/2)RT, Urms = √(3RT/M) and Urms ∝ 1/√M
∴ εav doesn't depend on its molecular mass.
According to the relation given above εav gets doubled when the temperature is increased 2 times. Thus option B is incorrect.
Hence, the correct option is A, C, and D.