The rms speed of an oxygen molecule in a sample at 300 K is about 480m/s. This does not mean that the speed of each molecule is 480 m/s. Many of the molecules have speed less than 480m/s and many have speed more than 480m/s. Maxwell derived an equation giving the distribution of molecules in different speeds. If dN represents the number of molecules with speeds between v and v+ dv then
The above figure shows plots of dN/dv against v at two different temperatures. We see that there are some molecules, which have speeds many times greater than the mean speed. This fact helps in making nuclear fusion reactions in a laboratory. The speed vp at which dN/dv is maximum, is called the most probable speed. Its value is
