Question

How can I prove this equation: `"mvr" = "nh"/(2π)`?

Answer 1

According to Bohr’s atomic model electron revolves around the nucleus in circular orbits.
As electron shows both wave and particle nature the circumference of circular orbit should by an integral multiple of wavelength (`λ`)

`"2πr = nλ"`

de-broglie wavelength (`lamda`) is given by

`λ = "h"/"mv"`

Substitute `λ = "h"/"mv"` in first equation

`"2πr = n" × "h"/"mv"`

On rearranging above equation

`"mvr" = "nh"/"2π"`

Answer 2

Quantisation of angular momentum is not something you prove as such. It is one of Bohr's postulates. Something that is just assumed to be true.