Question

For the Maxwell-Boltzmann speed distribution, the ratio of the root-mean-square speed (vrms) and the most probable speed (vmax) is
Given : Maxwell-Boltzmann speed distribution function for a collection of particles of mass m is
$f(v)=(\frac{m}{2\pi k_BT})^{3/2}4\pi v^2\text{exp}(-\frac{mv^2}{2k_BT})$
where, v is the speed and kBT is the thermal energy.

• A. $\sqrt{\frac{3}{2}}$
• B. $\sqrt{\frac{2}{3}}$
• C. $\frac{3}{2}$
• D. $\frac{2}{3}$

Answer 1

Answer: (A)

$\sqrt{\frac{3}{2}}$

Answer 2

The correct option is (A) : $\sqrt{\frac{3}{2}}$.