• # question_answer State Bohr's postulate for the permitted orbits for the electron in a hydrogen atom. Use this postulate to prove that the circumference of the nth permitted orbit for the electron can contain exact n wavelengths of the de-Broglie wavelength associated with the electron in that orbit.

Bohr's postulate of permitted orbits is only those circular orbits which are permitted for electron in which angular momentum of electron is an integral multiple of $h/2\pi .$ i.e.        $mvr=n\frac{h}{2\pi }$                         ?(i) where, n is an integer. From de-Broglie hypothesis, wavelength associated with electron, $\lambda =\frac{h}{mv}\Rightarrow mv=\frac{h}{\lambda }$ Substituting this value in Eq.(i), we get $\frac{h}{\lambda }r=n\frac{h}{2\pi }$             or         $2\pi r=n\lambda$ i.e. circumference $(S=2\pi r)$ of nth permitted orbit for the electron can contain exactly n wavelength of de-Broglie wavelength associated with electron in that orbit,