The ratio of the frequencies of the long wavelenght limits of Lyman and Balmer series of hydrogen spectrum is

Options

A. `27:5`
B. `5:27`
C. `4:1`
D. `1:4`

Answer

A

Explanation

For Lyman series, `n_(1)= 1, n_(2)=2`
`(1)/((lamda_("max"))_(1))= f_(1)= Rc [(1)/(1^(2))- (1)/(2^(2))]= (3Rc)/(4)`
For Balmer series,
`n_(1)= 2, n_(3)= 3`
`(1)/((lamda_("max"))_(2))= f_(2) = Rc [(1)/(2^(2))- (1)/(3^(2))] =(5Rc)/(36)`
`(f_(1))/(f_(2))= (3Rc)/(4) xx (36)/(5Rc) = (27)/(5)`