Question

The root mean square velocity of one mole of a monoatomic gas having molar mass $M$ is $u_{\text{rms}}$. The relation between the average kinetic energy $\left(E\right)$ of the gas and $u_{\text{rms}}$ is:

• A. $u_{\text{rms}}=\sqrt{\frac{3E}{2M}}$
• B. $u_{\text{rms}}=\sqrt{\frac{2E}{3M}}$
• C. $u_{\text{rms}}=\sqrt{\frac{2E}{M}}$
• D. $u_{\text{rms}}=\sqrt{\frac{E}{3M}}$

Answer 1

The correct option is C $u_{\text{rms}}=\sqrt{\frac{2E}{M}}$

Since, Relation between kinetic energy and $u_{\text{rms}}$ is given by:
$E=\frac{1}{2}M{u}_{\text{rms}}^2$
Hence,
$u_{rms}=\sqrt{\frac{2E}{M}}$