Question

If $\bar{v}, v_{rms}$ and $v_p$ represent the mean speed, root mean square and most probable speed of the molecules in an ideal monoatomic gas at temperature $T$ and if $m$ is mass of the molecule, then

• A. $v_{p} < v < v_{rms}$
• B. no molecule can have a speed greater than $\sqrt{2 v_{rms}}$
• C. no molecule can have a speed less than $v_p / \sqrt{2}$
• D. None of the above

Answer 1

Answer: (A)

Mean speed, $\bar{v}=\sqrt{\frac{8 k T}{\pi m}}=0.92 \,v_{ rms }$
rms speed, $v_{ rms }=\sqrt{\frac{3 k T}{m}}$
Most probable speed,
$v_{p}=\sqrt{\frac{2 k T}{m}}=0.816\, v_{ rms }$
So, $v_{p} < \bar{v} < v_{ rms }$