# Velocity sphere

by aaaa202
Tags: sphere, velocity
 PF Gold P: 956 It's the shell volume 4$\pi v^2 dv$ which is larger. If we imagine different vectors v, distributed as a uniform fine lattice of points in velocity-space, then the number of points in the shell will be proportional to the shell volume. I realise this 'answer' raises other issues, but I hope it is of some help.
 PF Gold P: 956 Velocity sphere Yes. Boltzmann (working before quantum theory) did effectively use a lattice of points, but it was arbitrary. How brilliant! Now we can justify the lattice quantum mechanically. In a crude treatment the molecules are matter waves of wavelength related to particle velocity by de Broglie's relation, $$mv=\frac{h}{\lambda}.$$ The wavelengths, $\lambda$, are fixed by boundary conditions for standing waves in a box. The lattice of points in velocity space emerges very simply from this.