The average kinetic energy of a gas molecule or atom at a given temperature is described by the kinetic theory of gases. The formula used to calculate the average kinetic energy (KE) of each particle in a gas is given by the equation:

$$ KE = \frac{3}{2} kT $$

where:

• $ k $ is the Boltzmann constant, and
• $ T $ is the absolute temperature in Kelvin.

This equation reveals that the average kinetic energy of any ideal gas particle depends only on the temperature, and not on the mass of the particles. Hence, at any given temperature, all ideal gas particles have the same average kinetic energy.

Given that both helium (He) and hydrogen molecule (H₂) are treated as ideal gases, at the same temperature of 298 K, the average kinetic energy of a helium atom would therefore be:

$$ KE_{\text{He}} = \frac{3}{2} k (298) $$

Similarly, for the hydrogen molecule:

$$ KE_{\text{H}_2} = \frac{3}{2} k (298) $$

It is evident that both expressions are identical, indicating that at 298 K, the average kinetic energy of a helium atom is the same as that of a hydrogen molecule. Despite the difference in mass between helium and hydrogen, conditions of temperature govern the kinetic energy within the framework of kinetic theory for ideal gases.

The correct answer is:

Option C: same as that of a hydrogen molecule