Question

Which of the following statements about Maxwell-Boltzmann law of distribution of molecular speeds are correct? This question has multiple correct options
A) The fraction of molecules having speed between c and (c+ dc) (regardless of direction) is given by: \[4\pi {\left( {\dfrac{M}{{2\pi RT}}} \right)^{3/2}}{c^2}\exp \left( {\dfrac{{M{c^2}}}{{2RT}}} \right)dc\].
B) The average speed is the arithmetic mean of the different speeds of all the molecules present in a given sample of the gas.
C) The speed distribution curve becomes sharper and is more peaked at a higher temperature as the average speed increases.
D) The speed distribution function is used to determine average molecular speeds.

Answer 1

Hint: According to Maxwell-Boltzmann law of distribution of molecular speeds, due to molecular collisions, the speed of gas molecules continuously changes. The collisions include the collisions between different gas molecules and the collisions with walls of containers.

Complete answer:
Due to the collisions, we should not consider the speed of individual molecules. Instead, we should consider the statistical average. This statistical average is the statistical average of speeds for the entire sample of gas. Thus, the average speed is not the arithmetic mean of the different speeds of all the molecules present in a given sample of the gas. The average speed is the statistical average.
Maxwell used probability theory to study the manner of distribution of gas molecules over various speed ranges. These speed ranges include from zero to very high. The law of distribution of molecular speeds summarizes the results of Maxwell’s study. The mathematical expression for this law is \[\dfrac{{dN}}{N} = 4\pi {\left( {\dfrac{M}{{2\pi RT}}} \right)^{3/2}}{c^2}\exp \left( {\dfrac{{M{c^2}}}{{2RT}}} \right)dc\]

Hence, the statements (A), (B) and (D) about Maxwell-Boltzmann law of distribution of molecular speeds are correct.

Note: With the help of Maxwell-Boltzmann law of distribution of molecular speeds, We can calculate the average velocity, rms velocity and most probable velocities of molecules. We also get an expression relating the average velocity, rms velocity and most probable velocities with each other.