Question

For a monoatomic gas, kinetic energy = $E$. The relation with $rms$ velocity is:

• A. $u=(\frac{2E}{m}{)}^{\frac{1}{2}}$
• B. $u=(\frac{3E}{2m}{)}^{\frac{1}{2}}$
• C. $u=(\frac{E}{2m}{)}^{\frac{1}{2}}$
• D. $u=(\frac{E}{3m}{)}^{\frac{1}{2}}$

Answer 1

Answer: (A)

$u=(\frac{2E}{m}{)}^{\frac{1}{2}}$

The expression for the kinetic energy of a monoatomic gas is $\left(E\right)=\frac{3}{2}kT$.
The expression for the kinetic energy is $=\sqrt{\frac{3kT}{m}}$.
Thus, the rms velocity is given as:

$u=\sqrt{\frac{2E}{m}}$.