(i) State Bohr's quantization condition for defining stationary orbits . How does de- Broglie hypothesis explain the stationary orbits ?
(ii) find the relation beween the three wavelengths
`lambda_(1), lambda _(2) " and " lambda_(3)` from the energy level diagram shown :

Explanation

(i) Electrons can revolve in those stationary orbits in which their angular momentum is integral multiple of `h//2pi`
`i.e., " ""mvr " = nh//2pi`
for electron in an atom de-Broglie proposed that wave like nature exist in the form of standing waves i.e., wave is associated with electron moving in a shell only certain discrete frequencise will have a wavelength that will fit exactly around the nucleus i.e.,
`2pi r = n lambda " ""but "" "lambda =h//mv`
`2pir=(nh)/(mv)" "`
`rArr h((h)/(2pi)) = ` mvr which is Boh's postulate
(ii) `E_(CA) =E_(CB) + E_(BA) " "," "(hc)/(lambda_(3)) =(hc)/(lambda_(1) )+(hc)/(lambda_(2))`
`rArr " "(1)/(lambda_(3))=(1)/(lambda_(1))+(1)/(lambda_(2))" "rArr " "lambda_(3) =(lambda_(1).lambda_(2))/(lambda_(1)+lambda_(2))`