JEE Main 2025 · 7 April · evening · Single correct · +4 / −1

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:
(Give: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol)

  1. (a) 1 : √10
  2. (b) 10 : 1
  3. (c) 1 : 10
  4. (d) 1 : 1
Answer and solution

Answer (d) 1 : 1

Solution

Physics sir · 4 steps

Average kinetic energy per molecule depends only on temperature, so the mass of the gas does not matter here.

  1. Monatomic gases. Helium and argon are both monatomic. Each atom has only 3 translational degrees of freedom.
  2. Equipartition. Each degree of freedom carries 1/2k_BT on average. So with 3 of them, the average kinetic energy per molecule is:

    Ē = 3/2k_BT

  3. Mass drops out. This expression has no molar mass in it. Argon atoms are 10 times heavier, but they move slower in exactly the right way to keep 1/2mv² the same.
  4. So. Both gases are at 300 K and have the same degrees of freedom, so Ē_(He) : Ē_(Ar) = 1 : 1, which is option (d).

The idea to keep. At the same temperature, gases with the same degrees of freedom have the same average kinetic energy per molecule. Mass changes the speed, not the energy.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Kinetic Theory of Gases

Asked about 130 times in JEE Main since 2020. This question is from 2025.