A hydrogen atom emits a photon of wavelength `36/(35R)` when it is jumped from its nth excited state to the ground state. Then the quantum number n is
(R is Rydberg constant.)

Options

A. 8
B. 7
C. 5
D. 6

Answer

D

Explanation

Key Idea When a electron jump from `n^(th)` state to ground state, then the lyman-series of hydrogen spectrum will appear.
Given wavelength, `lambda_(n^(th))=36/(35R)`
As wavelength in lyman-series,
`" "I/lambda_(Ly)=R[1-1/n^(2)]" "(because n=2, 3, 4)`
`rArr " "lambda_(Ly)=n^(2)/(R(n^(2)-1))`
Where, `lambda_(Ly)` is the wavelength of the photon, when a electron jumps from `n^(th)` state to ground state.
Hence, `lambda_(Ly)=lambda_(n^(th))`
`rArr n^(2)/(R(n^(2)-1))=36/(35R) rArr n^(2) =36 rArr n=6^(th)` state.