Question

Which of the following statements about Maxwell-Boltzmann law of distribution of molecular speeds are correct?

• A. The fraction of molecules having speed between c and $(c+dc)$ (regardless of direction) is given by: $4\pi {\left(\frac{M}{2\pi RT}\right)}^{3/2}{c}^{2}exp\left(\frac{M{c}^2}{2RT}\right)dc$.
• 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

Answer: (A), (B), (D)

The correct options are
A The fraction of molecules having speed between c and $(c+dc)$ (regardless of direction) is given by: $4\pi {\left(\frac{M}{2\pi RT}\right)}^{3/2}{c}^{2}exp\left(\frac{M{c}^2}{2RT}\right)dc$.
B The speed distribution function is used to determine average molecular speeds.
D The average speed is the arithmetic mean of the different speeds of all the molecules present in a given sample of the gas.

According to this theory,

• The speed of a molecule of a gas changes continuously as a result of collisions with other molecules and with the walls of the container. Thus, the net result is that we cannot speak of the speed of individual molecule; hence must consider the statistical averages of the speeds of the whole collection of gas molecules.
• The manner in which the molecules of a gas are distributed over the possible speed ranges, from zero to very high values, was first investigated by Maxwell using the theory of probability. His results are expressed as the law of distribution of molecular speeds, one form of which is

$dN/N=4\pi {\left(\frac{M}{2\pi RT}\right)}^{3/2}{c}^{2}exp\left(\frac{M{c}^2}{2RT}\right)dc$

Option A, B and D are correct.