Given the same room temperature of 300 K for helium and argon, we are tasked with finding the ratio of their average kinetic energies per molecule.

Formula for Kinetic Energy per Molecule:
K.E.

In this equation:
is the degrees of freedom, which is 3 for both helium (He) and argon (Ar) since they are monatomic gases.
is the Boltzmann constant.
is the temperature in Kelvin.

Kinetic Energy Comparison:
For both helium and argon, since , the

expression simplifies:

Thus, the average kinetic energy per molecule for both gases is the same at the same temperature, leading to a ratio of:

This result implies that despite their differences in molar masses (helium being and argon ), the average kinetic energy per molecule remains equal at the same temperature.