1. Degrees of freedom of a non-rigid diatomic molecule

A non-rigid diatomic molecule has the following active degrees of freedom at ordinary temperatures:

• $3$ translational
• $2$ rotational
• $2$ vibrational

So total degrees of freedom: $f = 3+2+2 = 7$

2. Average energy per molecule

By the equipartition theorem, each degree of freedom contributes $\frac{1}{2}k_B T$ to the energy.

Hence, energy per molecule is $E_1 = \frac{f}{2}k_B T = \frac{7}{2}k_B T$

3. Energy of 10 molecules

For $10$ molecules, $E = 10 \times \frac{7}{2}k_B T = 35 k_B T$

4. Match with options

The obtained answer is $35 k_B T$

This matches Option D.

5. Check other options

• A: $35RT$ → wrong, because $R$ is used for one mole, not for 10 molecules.
• B: $\frac{7}{2}RT$ → wrong, this is not for 10 molecules and also uses $R$ incorrectly.
• C: $70k_B T$ → wrong, double the correct value.
• D: $35k_B T$ → correct.

Therefore, the correct answer is D.