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





Q.32:- Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.

 

 

Answer:-
According to Bohr postulate of angular momentum,
mvr = nh/2π ⇒ 2πr = nh/mv   …(i)
According to de Broglie equation, λ=h/mv   …(ii)
Substituting the value of eqn (ii) in eqn (i) we get,
2πr = nλ
Thus, circumference of the Bohr orbit for the hydrogen atom is an integral multiple of de Broglie’s wavelength associated with the electron revolving around the orbit.