What is the ratio of shortest wavelength of the Balmer series ot the shortest waelength of the Lyman series?

Options

A. `4:1`
B. `4:3`
C. `4:9`
D. `5:9`

Answer

A

Explanation

For a Balmer series, `(1)/(lambda_(B))=R[(1)/(2^(2))-(1)/(n^(2))]" ….(i)"`
where `n=3,4,…..`
By putting `n=oo` in equation (i), we obtain the series limit of the Balmer series. This is the shortest wavelength of the Balmer series.
`"or "lambda_(B)=(4)/(R )" ...(ii)"`
For a Lyman series, `(1)/(lambda_(L))=R[(1)/(1^(2))-(1)/(n^(2))]" ....(iii)"`
where `n=2,3, 4,.........`
By putting `n=oo` in equation (iii), we obtain the series limit of the Lyman series. This is the shortest wavelength of the Lyman series.
or `lambda_(L)=(1)/(R )`
Dividing (ii) by (iv), we get `(lambda_(B))/(lambda_(L))=(4)/(1)`