Question

Question #6756e

Answer 1

See below.

Explanation:

The Maxwell-Boltzmann distribution has a number of applications, but one is in determining the distribution of kinetic energy for a set of molecules. This works because the distribution of kinetic energy is identical to the distribution of the speeds for a certain gas at any temperature.

Since this is a probability distribution, it can be characterized according to its width (among other things). The width of the distribution characterizes the most likely range of speeds for the particles.

One measure of the width is the Full Width at Half Maximum (FWHM). To determine this value, find the height of the distribution at the most probable speed `v_p` (maximum height, see diagram). Divide this value by two to obtain the half height, and locate the two speeds in the distribution which have this half-height value. One speed will be greater than `v_"p"` and the other will be smaller. The full width is the difference between these two speeds at the half-maximum value.

See Maxwell Distribution Laws for more information on this distribution.