State the expression for the radius of the nth Bohr orbit in a hydrogen atom. Hence state the expression for the de Broglie wavelength associated with the electron in this orbit.

Explanation

The radius of the nth Bohr orbit is
`r=(epsi_0h^2n^2)/(pime^2)`
If `lamda` is the Broglie wavelength associated with the electron in the nth orbit `2pir-nlamda`
`therefore lamda=(2pir)/(n)=(2pi)/(n)((epsi_0h^2n^2)/(pime^2))=(2epsi_0h^2n)/(me^2)`