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MCQEasyJEE 2025Molecular Speeds (rms, Average, Most Probable)

JEE Physics 2025 Question with Solution

The ratio of vapour densities of two gases at the same temperature is 425\frac{4}{25}, then the ratio of r.m.s. velocities will be:

  • A

    254\frac{25}{4}

  • B

    25\frac{2}{5}

  • C

    52\frac{5}{2}

  • D

    425\frac{4}{25}

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: The ratio of vapour densities of two gases at the same temperature is

ρ1ρ2=425\frac{\rho_1}{\rho_2} = \frac{4}{25}

Find: The ratio of r.m.s. velocities v1v2\frac{v_1}{v_2}.

The r.m.s. velocity of a gas is inversely proportional to the square root of its molecular mass. Vapour density is directly proportional to the molecular mass.

So,

v1v2=ρ2ρ1\frac{v_1}{v_2} = \sqrt{\frac{\rho_2}{\rho_1}}

Substituting the given vapour density ratio,

v1v2=254=52\frac{v_1}{v_2} = \sqrt{\frac{25}{4}} = \frac{5}{2}

Therefore, the ratio of r.m.s. velocities is 52\frac{5}{2}. The correct option is C.

Common mistakes

  • Using vapour density as directly proportional to r.m.s. velocity is incorrect because r.m.s. velocity is inversely proportional to the square root of molecular mass. Use the inverse square-root relation instead.

  • Taking v1v2=ρ1ρ2\frac{v_1}{v_2} = \sqrt{\frac{\rho_1}{\rho_2}} is wrong because it reverses the dependence. Since heavier gas moves slower, the correct form is v1v2=ρ2ρ1\frac{v_1}{v_2} = \sqrt{\frac{\rho_2}{\rho_1}}.

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