Given below are two statements :
Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature.
Statement II : The rms speed of oxygen molecules in a gas is v. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become 2 v.
In the light of the above statements, choose the correct answer from the options given below :

Solution

Physics sir · 4 steps

Momentum is a vector, so random motion averages it to zero. Then track both T and M in the rms speed.

1. Statement I. Momentum has a direction. In an ideal gas at rest, molecules move equally in all directions, so their momentum vectors cancel. The average momentum is zero at every temperature, so it does not depend on temperature. Statement I is false.
2. Rms speed formula. The rms speed depends on both temperature and molar mass, so check how each one changes.

   vᵣₘₛ = √(3RT/M)

3. Statement II. Doubling the temperature makes T → 2T. Splitting O₂ into O atoms halves the molar mass, M → M/2. So T/M becomes 2T/(M/2) = 4T/M, and vᵣₘₛ becomes √4 v = 2v. Statement II is true.
4. So. Statement I is false and Statement II is true, which is option (d).

The idea to keep. Average speed grows with √T, but average momentum (a vector) is always zero for a gas at rest. For rms speed, always check whether both T and M change.

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