Show that the circumference fo the Bohr orbit for the hydrogen atom is an integral multiple of the de-Broglie wavelength associated with the electron revolving around the orbit.

Explanation

For Bohr.s model angular momentum of element is
`m_(e) vr = (nh)/( 2pi)`
circumference `=2pi r = (nh)/( m_(e ) v)`
and `m_( e) v= (nh)/( 2pi r)`
According ot de - broglie
`lambda = (h)/(mv) ` and mv `=(h)/(lambda) `
as (i) and (ii)
mv = `(nh)/( 2pi r) = (h)/( lambda ) :., (n)/(2pi r) = (1)/(lambda) :. , 2pi r = n lambda` Bohr.s orbit circumference `(2pi r ) = n ` de- Broglie wavelength
In this way de broylic wave length is associated wth Bohr.s orbit circumference.