The average thermal energy for a mono-atomic gas is: ($k_{B}$ is Boltzmann constant and $T$ is absolute temperature)

Given below are two statements:
Statement $I :$ In a diatomic molecule,the rotational energy at a given temperature obeys Maxwell's distribution.
Statement $II :$ In a diatomic molecule,the rotational energy at a given temperature equals the translational kinetic energy for each molecule.
In the light of the above statements,choose the correct answer from the options given below:

Energy of $10$ non-rigid diatomic molecules at temperature $T$ is:

Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of $T$. The total internal energy,$U$ of a mole of this gas,and the value of $\gamma \left( = \frac{C_P}{C_V} \right)$ are given,respectively,by:

The value of $\gamma \left( = \frac{C_{p}}{C_{v}} \right)$ for hydrogen,helium,and another ideal diatomic gas $X$ (whose molecules are not rigid but have an additional vibrational mode) are respectively equal to:

$A$ polyatomic gas with $n$ degrees of freedom has a mean energy per molecule given by (where $k$ is Boltzmann's constant and $T$ is temperature).