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 $2v$.
In the light of the above statements, choose the correct answer from the options given below :
Answer: (D) Statement I is false but Statement II is true
Statement I: Molecules move in random directions, so the average momentum (a vector) is zero at every temperature. False.
Statement II: $v_{\text{rms}} = \sqrt{\dfrac{3RT}{M}}$. Doubling $T$ and halving $M$ (O$_2$ to O) multiplies it by $\sqrt{4} = 2$. True.
Solution by Sreeraj P, M.Sc Physics