An excited hydrogen atom emits a photon of wavelength `lambda` in returning to the ground state. If R is the Rydberg constant, then the quantum number n of the excited state is

Options

A. `sqrt(lambda R)`
B. `sqrt(lambda R-1)`
C. `sqrt(lambda (lambdaR-1))`
D. `sqrt((lambda R)/(lambdaR-1))`

Answer

D

Explanation

`1/lambda =R_H(1/1^2 -1/n^2)`
`1-1/n^2 =1/(R_H lambda) =(lambdaR_H-1)/(lambdaR_H)`
`n^2 =(lambdaR_H)/(lambdaR_H-1)`
`:. n = sqrt((lambdaR_H)/(lambdaR_H-1))`