An excited state of H atom emits a photon of wavelength `lamda` and returns in the ground state. The principal quantum number of excited state is given by:

Options

A. `lamdaR(R-1)`
B. `sqrt(lamdaR(R+1))`
C. `sqrt((lamdaR)/(lamdaR-1))`
D. `sqrt((lamda R-1)/(lamdaR))`

Answer

C

Explanation

`1/lamda = R [1/1^1 - 1/n^2] = R - R/n^2`
`therefore R/n^2 = R - 1/lamda = (lamdaR - 1)/(lamda)`
`therefore n^2 = (lamdaR)/(lamdaR - 1) therefore n = sqrt((lamdaR)/(lamdaR-1))`