Two identical containers contain helium and neon gas respectively at the same temperature and pressure. The ratio of the root mean square speeds of the helium atoms to the neon atoms is

Solution

1. The root mean square speed is given by the formula $v_{rms}=\sqrt{\frac{3RT}{M}}$, where $M$ is the molar mass.
2. Since $T$ is constant, the ratio of the speeds is $v_{He}/v_{Ne}=\sqrt{M_{Ne}/M_{He}}$.
3. The molar mass of helium is $4\text{ g/mol}$ and the molar mass of neon is $20\text{ g/mol}$.
4. Substituting these values gives $\sqrt{20/4}=\sqrt{5}$.
5. Hence the answer is (A).