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

Options

A. `sqrt((lamda R)/(lamda R-1))`
B. `sqrt((lamda)/(lamda R-1))`
C. `sqrt((lamda R^(2))/(lamda R-1))`
D. `sqrt((lamda R)/(lamda-1))`

Answer

A

Explanation

`(1)/(lamda) = R ((1)/(n_(1)^(2))- (1)/(n_(2)^(2)))`
`rArr (1)/(lamda) = R (1- (1)/(n^(2))) rArr 1- (1)/(n^(2))= (1)/(lamda R)`
`rArr (1)/(n^(2))= 1- (1)/(lamda R) rArr n= sqrt((lamda R)/(lamda R-1))`