The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is : (Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol)

For an ideal gas, the average translational kinetic energy of one molecule at absolute temperature $$T$$ is given by the expression

$$\overline{E_k} = \frac{3}{2}\,k\,T$$

Here, $$k$$ is the Boltzmann constant and $$T$$ is the thermodynamic temperature. Observe that $$\overline{E_k}$$ depends only on the temperature and the universal constant $$k$$; it is independent of the nature, molar mass, or molecular mass of the gas.

Both helium and argon are in the same flask at the same temperature $$T = 300 \text{ K}$$. Therefore, their average kinetic energies per molecule are equal:

$$\overline{E_k}(\text{He}) = \frac{3}{2}\,k\,T$$
$$\overline{E_k}(\text{Ar}) = \frac{3}{2}\,k\,T$$

The required ratio is

$$\frac{\overline{E_k}(\text{He})}{\overline{E_k}(\text{Ar})} = \frac{\frac{3}{2}\,k\,T}{\frac{3}{2}\,k\,T} = 1$$

Hence, the ratio of average kinetic energies (per molecule) of helium to argon is $$1 : 1$$.

The correct choice is Option D.