Ratio of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is

Options

A. `(7)/(29)`
B. `(9)/(31)`
C. `(5)/(27)`
D. `(3)/(23)`

Explanation

The wavelength of different spectral lines of Lyman series given by
`(1)/(lambda_(L))=R[(1)/(1^(2))-(1)/(n^(2))]" where "n=2,3, 4,…….`
Where subscript L refers to Lyman.
For longest wavelength, n = 2
`therefore" "(1)/(lambda_(L_("longest")))=R[(1)/(1^(2))-(1)/(n^(2))]" where "n = 2, 3, 4, ..........`
Where subscripit L refers to Lyman.
For longest wavelength, n = 2
`therefore" "(1)/(lambda_(L_("longest")))=[(1)/(1^(2))-(1)/(2^(2))]=(3)/(4)R" ...(i)"`
The wavelength of different spectral series of Balmer series is given by
`(1)/(lambda_(B))=R[(1)/(2^(2))-(1)/(n^(2))]` where `n=3, 4, 5, .........`
where subscript B refers to Balmer.
For longest wavelength, n = 3
`therefore" "(1)/(lambda_(B_("longest")))=R[(1)/(2^(2))-(1)/(3^(2))]=R[(1)/(4)-(1)/(9)]=(5R)/(36)" ...(ii)"`
Divide (ii) by (i), we get
`(lambda_(L_("longest")))/(lambda_(B_("longest")))=(5R)/(36)xx(4)/(3R)=(5)/(27)`