The root mean square speed of gas molecules is given by which expression?

Solution

1. The root mean square speed ($v_{rms}$) represents the square root of the average of the squares of the individual molecular speeds.
2. According to the kinetic molecular theory of gases, the pressure exerted by an ideal gas is related to the average kinetic energy of its molecules.
3. By equating the kinetic energy expression to the thermal energy of the gas, we derive the formula $v_{rms}=\sqrt{\frac{3RT}{M}}$, where $R$ is the universal gas constant, $T$ is the absolute temperature, and $M$ is the molar mass.
4. Hence the answer is (B).