Question

The root mean square velocity of one mole of a monatomic gas having molar mass $M$ is $U_{ rms }$. The relation between the average kinetic energy $(E)$ of the gas and $U_{rm s}$ is

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

Answer 1

Answer: (C)

Average kinetic energy,
$E=\frac{3}{2} R T$ ...(i)
Root mean square velocity,
$U_{ rms }=\sqrt{\frac{3 R T}{M}}$
From eq. (i),
$R T=\frac{2 E}{3}$
On putting the value of $R T$ in the expression of $U_{ rms }$, we get
$U_{ rms }=\sqrt{\frac{3 \times 2 E}{3 M}}=\sqrt{\frac{2 E}{M}}$