A hydrogen atom ia in excited state of principal quantum number `n` . It emits a photon of wavelength `lambda` when it returnesto the ground state. The value of `n` is

Options

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

Answer

C

Explanation

Energy of photon `E=Rhc(1-(1)/(n^(2)))`
or `(hc)/(lamda)=Rch(1-(1)/(n^(2))) or (1)/(lamda)=R(1-(1)/(n^(2)))`
or `(1)/(lamda R)=1-(1)/(n^(2)) or (1)/(n^(2))=1-(1)/(lamdaR)`
or `=((lamdaR-1))/(lamdaR)`
or `n=sqrt((lamdaR)/((lamdaR-1)))`