Question

The root mean square velocity of a monoatomic gas (molar mass $=m{\text{kg mol}}^{-1}$) is $u$. Its kinetic energy per mole $\left(E\right)$ is related to $u$ by equation:

• A. $u=\sqrt{\frac{3E}{m}}$
• B. $u=\sqrt{\frac{2E}{m}}$
• C. $u=\sqrt{\frac{2E}{3m}}$
• D. $u=\sqrt{\frac{E}{3m}}$

Answer 1

The correct option is B $u=\sqrt{\frac{2E}{m}}$

$u=\sqrt{\frac{3RT}{m}},\text{KE}=E=\frac{3}{2}RT$
Thus, $RT=\frac{2}{3}E$
$u=\sqrt{\frac{3RT}{m}}=\sqrt{\frac{3\times 2E}{3m}}=\sqrt{\frac{2E}{m}}$