Question

What are the most probable velocity and the average velocity for a system that follows the Maxwell-Boltzmann distribution?

Answer 1

Maxwell-Boltzmann distribution:

• The Maxwell-Boltzmann distribution is frequently depicted in the graph below.
• The y-axis of the Maxwell-Boltzmann graph represents the number of molecules per unit speed.
• So, if the graph in a specific region is higher, it suggests there are more gas molecules traveling at those rates.

Most probable velocity :

• The most likely velocity is the velocity possessed by the greatest fraction of molecules at the same temperature is most probable velocity.
• ${\mathrm{c}}_{\mathrm{mp}}=\sqrt{\frac{2.\mathrm{R}.\mathrm{T}}{\mathrm{M}}}$
• Here, R is the gas constant, T is the temperature, and, M is the molar mass of the gas.

Average velocity :

• The average velocity is the displacement divided by the total time. We compute the expected value of v.
• $C_{\mathit{\text{average}}}=\sqrt{\frac{8.\mathrm{R}.\mathrm{T}}{\mathrm{\pi }.\mathrm{M}}}$