Question

A helium atom is two times heavier than a hydrogen molecule. At $300$ K, the average kinetic energy of a helium atom is:
A) $\dfrac{1}{2}$ of ${H_2}$ molecules
B) Two times that of ${H_2}$molecules
C) Four times of ${H_2}$ molecules
D) Same as that of ${H_2}$ molecules

Answer 1

Hint: Temperature is that the only variable on which the K.E. of a perfect gas depends. The energy isn't full of the mass of the molecules. Going by the perfect gas law ($PV = nRT$ ), If changes in pressure and/or volume lead to temperature changes, it means the typical K.E. of the molecules has been changed.Where ‘P’ is pressure ,’T’ is the temperature, ‘n’ is number of moles, ’V’ is the volume and ‘R’ is universal gas constant

Complete step by step answer:
In a gas, there aren't any attractive forces between the gas molecules, and there's no rotation or vibration within the molecules.
The basic version of the model describes the ideal gas and considers no other interactions between the particles and, thus, the character of K.E. transfers during collisions are strictly thermal.
The temperature of a perfect gas is proportional to the common mechanical energy per gas molecule.
The formula for the energy of a gas defines the common K.E. per molecule. The energy is measured in Joules (J), and also the temperature is measured in Kelvin (K).

$KE = \dfrac{3}{2}RT$

Kinetic energy per mole or per molecule of a gas depends only on the temperature and not on the character of the gas. Since the temperature of both the gases is that the same within the expression

So, the typical K.E. of a helium atom is identical to that of a hydrogen molecule.

So, the correct answer is Option D .

Note: Temperature and pressure are macroscopic properties of gases. These properties are associated with molecular motion, which could be a microscopic phenomenon. The scientific theory of gases correlates between macroscopic properties and microscopic phenomena. Kinetics means the study of motion and in this case motions of gas molecules.
At the identical temperature and volume, the identical numbers of moles of all gases exert identical pressure on the walls of their containers. This can be called Avogadro's principle. His theory implies that the identical numbers of moles of gas have an identical number of molecules.
Avogadro's principle also implies that the kinetic energies of varied gases are identical at the identical temperature. The molecular masses are different from gas to gas, and if all gases have the identical average K.E., the common speed of a gas is exclusive.