Question

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
(a) v
(b) $v\sqrt{2}$
(c) 2v
(d) 4v.

Answer 1

$$\begin{gathered} \mathrm{Given}:\mathrm{v}=\sqrt{\frac{3\mathrm{RT}}{32}} \\ \mathrm{Let}\mathrm{the}\mathrm{new}\mathrm{rms}\mathrm{speed}\mathrm{be}\mathrm{v}\text{'}. \\ \mathrm{Molecule}\mathrm{dissociate},M=16 \\ v\text{'}=\sqrt{\frac{3R\left(2T\right)}{16}} \\ =\sqrt{\frac{3R\left(4T\right)}{32}} \\ =2\sqrt{\frac{3RT}{32}}=2v \end{gathered}$$

Thus, (c) is the correct answer.