Why do lighter gas molecules move faster than heavier molecules at the same temperature?

According to the kinetic theory of gases, the temperature of a gas is directly related to the average kinetic energy of its molecules. This relationship is expressed by the formula:

$$\frac{1}{2}m{v}^2=\frac{3}{2}kT$$

In this equation, $m$ represents the mass of the molecule, $v$ is its velocity, $k$ is the Boltzmann constant, and $T$ is the absolute temperature.1

Because the average kinetic energy depends only on the temperature, it remains constant for all gases at the same temperature. Consequently, if the mass ($m$) of a gas molecule is smaller, its velocity ($v$) must be higher to maintain the same average kinetic energy. This principle explains why lighter gas molecules move faster than heavier ones under identical thermal conditions.1