To determine the average thermal energy for a mono-atomic gas, we use the concept of degrees of freedom.$\\$For a mono-atomic gas, there are 3 translational degrees of freedom.$\\$According to the equipartition theorem, each degree of freedom contributes $\frac{1}{2} k_B T$ to the energy.$\\$Therefore, the total average thermal energy for a mono-atomic gas is:$\\ E = \frac{1}{2} k_B T \times 3 \\ E = \frac{3}{2} k_B T \\$Thus, the average thermal energy for a mono-atomic gas is $\frac{3}{2} k_B T$, which corresponds to Option 1.