1. Use the equipartition theorem

For a system in thermal equilibrium at temperature $T$, each independent quadratic degree of freedom contributes an average energy of

$\frac{1}{2}k_B T$

per molecule.

2. Degrees of freedom for a monoatomic gas

A monoatomic gas molecule can only have 3 translational degrees of freedom:

• motion along $x$
• motion along $y$
• motion along $z$

So, total degrees of freedom:

$f = 3$

3. Average energy per molecule

Hence, the average energy of one molecule is

$\langle E \rangle = \frac{f}{2}k_B T = \frac{3}{2}k_B T$

4. Match with the options

• A: $\frac{3}{2}k_B T$ ✅
• B: $k_B T$ ❌
• C: $\frac{2}{3}k_B T$ ❌
• D: $\frac{1}{2}k_B T$ ❌

Therefore, the correct option is A.