If `lamda_(1)andlamda_(2)` are the wavelength of the photons emitted, when electrons in the `n^(th)` orbit of hydrogen atom fall to first excited state and ground state respectively, then the value of n is

Options

A. `sqrt((2(lamda_(2)-lamda_(1)))/(2lamda_(2)-lamda_(1)))`
B. `sqrt((2lamda_(2)-lamda_(1))/(2(lamda_(2)-lamda_(1))))`
C. `sqrt((4lamda_(2)-lamda_(1))/(4(lamda_(2)-lamda_(1))))`
D. `sqrt((4(lamda_(2)-lamda_(1)))/((4lamda_(2)-lamda_(1))))`

Answer

D

Explanation

We have,
`lamda_(1)=(hc)/(DeltaE_(nto2))andlamda_(2)=(hc)/(DeltaE_(nto1))`
`rArrlamda_(1)(13.6/4-13.6/n^(2))=lamda_(2)(13.6/1-13.6/n^(2))`
`rArr" "n=sqrt((4(lamda_(2)-lamda_(1)))/(4lamda_(2)-lamda_(1)))`