1. Average kinetic energy of a gas molecule

   For any ideal gas, the average translational kinetic energy per molecule is $\bar{K} = \frac{3}{2}kT$ where:

   • $k$ = Boltzmann constant
   • $T$ = absolute temperature

2. Compare helium and argon

   Both helium and argon are at the same temperature: $T = 300\,\text{K}$

   Therefore, $\bar{K}_{\text{He}} = \frac{3}{2}kT$ and $\bar{K}_{\text{Ar}} = \frac{3}{2}kT$

3. Take the ratio

   $\bar{K}_{\text{He}} : \bar{K}_{\text{Ar}} = \frac{3}{2}kT : \frac{3}{2}kT = 1:1$

4. Important concept

   Average kinetic energy depends only on temperature, not on molar mass. The given molar masses are irrelevant for this question.

5. Check options

   • A: $1 : \sqrt{10}$ $\rightarrow$ incorrect
   • B: $10 : 1$ $\rightarrow$ incorrect
   • C: $1 : 10$ $\rightarrow$ incorrect
   • D: $1 : 1$ $\rightarrow$ correct

Therefore, the correct option is D.