The rms speed of the molecules of a gas in a vessel is 400 ms⁻¹. If half of the gas leaks out at constant temperature, the rms speed of the remaining molecules will be

The correct option is 400 ms⁻¹.

To understand why the root mean square (rms) speed remains unchanged, let us look at the formula for the rms speed of gas molecules:
$v_{\text{rms}}=\sqrt{\frac{3RT}{M}}$
where:
• $R$ is the universal gas constant,
• $T$ is the absolute temperature of the gas, and
• $M$ is the molar mass of the gas.

From this relation, it is clear that the rms speed of the gas molecules depends solely on the absolute temperature ($T$) and the nature of the gas (molar mass, $M$). It is completely independent of the total mass of the gas or the number of molecules present in the container.

Since the problem specifies that half of the gas leaks out at a constant temperature, both the temperature $T$ and the molar mass $M$ of the remaining gas molecules remain unchanged.

Therefore, the rms speed of the remaining molecules remains unchanged:
$v_{\text{rms}}=400{\text{ms}}^{-1}$