NEET 2020 Physics Question 162 Solution

A monoatomic gas molecule (such as Helium, Neon, or Argon) behaves as a point mass. It can move freely in 3 independent spatial directions (along the x, y, and z Cartesian axes), giving it 3 translational degrees of freedom ($$f = 3$$). It has negligible moment of inertia about its own center, so rotational degrees of freedom are absent.

According to Boltzmann's Law of Equipartition of Energy, in thermal equilibrium at absolute temperature $$T$$, the average energy associated with each independent degree of freedom per molecule is: $$E_{\text{per mode}} = \frac{1}{2} k_B T$$, where $$k_B$$ is Boltzmann's constant.

Multiplying the energy per mode by the total number of degrees of freedom ($$f = 3$$): $$E_{\text{avg}} = 3 \times \left(\frac{1}{2} k_B T\right) = \frac{3}{2} k_B T$$.

Therefore, the average thermal energy of a monoatomic gas atom is $$\frac{3}{2} k_B T$$, matching Option 2.