The electron in a hydrogen atom jumps back from an excited state to ground state, by emitting a photon of wavelength `lambda_(0) = (16)/(15R)`, where R is Rydbergs's constant. In place of emitting one photon, the electron could come back to ground state by

Options

A. Emitting `3` photons of wavelength `lambda_(1), lambda_(2)` and `lambda_(3)` such that `(1)/(lambda_(1)) + (1)/(lambda_(2)) + (1)/(lambda_(3)) = 15R/16`
B. Emitting `2` photons of wavelength `lambda_(1), lambda_(2)` and `lambda_(3)` such that `(1)/(lambda_(1)) + (1)/(lambda_(2)) + (1)/(lambda_(3)) = 15R/16`
C. Emitting 2 photons of wavelength `lambda_(1)` and `lambda_(2)` such that `lambda_(1) + lambda_(2) = 16/15R`
D. Emitting `3` photons of wavelength `lambda_(1), lambda_(2)` and `lambda_(3)` such that `lambda_(1) + lambda_(2) + lambda_(3) = 16/15R`

Answer

A, B

Explanation

`(1)/(lambda_(0)) = R[(1)/(1^(2)) - (1)/(n^(2))], n = 4`
(a) `(hc)/(lambda_(0)) = (hc)/(lambda_(1)) + (hc)/(lambda_(2)) rArr (1)/(lambda_(0)) = (1)/(lambda_(1)) + (1)/(lambda_(2))`
or ` (hc)/(lambda_(0)) = (hc)/(lambda_(1)) + (hc)/(lambda_(2)) + (hc)/(lambda_(3)) rArr (1)/(lambda_(0)) = (1)/(lambda_(1)) + (1)/(lambda_(2)) + (1)/(lambda_(3))`