Question

For the Maxwell-Boltzmann speed distribution, the ratio of the root-mean-square speed (v_rms) and the most probable speed (v_max) 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 k_BT is the thermal energy.

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

Answer 1

The Correct Option is A

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