JEE Main 2024 · 8 April · evening · Single correct · +4 / −1
Given below are two statements :
Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter.
Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.
In the light of the above statements, choose the correct answer from the options given below :
- (a) Statement I is false but Statement II is true
- (b) Both Statement I and Statement II are true
- (c) Statement I is true but Statement II is false
- (d) Both Statement I and Statement II are false
Answer and solution
Answer (b) Both Statement I and Statement II are true
Solution
Physics sir · 4 steps
Check each statement against its formula: λ has d² downstairs, and average KE is 3/2kT.
- Mean free path. A molecule of diameter d collides with any molecule whose centre comes within d of its own. So it sweeps out a collision cross-section of area π d², and a bigger area means more collisions and a shorter free path.
λ = 1/(√2 π d² n) = (k T)/(√2 π d² P)
- Statement I. With the other quantities fixed, λ ∝ 1/d². Doubling the diameter cuts the mean free path to one quarter. Statement I is true.
- Statement II. Kinetic theory gives the average translational kinetic energy per molecule as 3/2kT, where k is Boltzmann's constant. So the average KE is directly proportional to the absolute temperature T. Statement II is true.
- So. Both statements are true, which is option (b).
The idea to keep. Mean free path falls as 1/d² because collisions depend on the area π d², not on d. Average KE depends only on T in kelvin, never on °C.
Answer from the NTA final answer key. Solution by PrepWiser.