If `lambda_(1)` and `lambda_(2)` are the wavelengths of the first members of the Lyman and Paschen series respectively, then `lambda_(1) : lambda_(2)` is

Options

A. `1:3`
B. `1:30`
C. `7:50`
D. `7:108`

Answer

D

Explanation

For Lyman series , `n_(1)=1` and `n_(2)=2` for first line.
`therefore (1)/(lambda_(1))=R[(1)/(1^(2))-(1)/(2^(2))]=R[(1)/(1)-(1)/(4)]=(3R)/(4)`
For Paschen series, `n_(1)=3` and `n_(2)=4` for `1^(st)` line.
`therefore (1)/(lambda_(2))=R[(1)/(3^(2))-(1)/(4^(2))]=R[(1)/(9)-(1)/(16)]=(7R)/(144)`
`(lambda_(1))/(lambda_(2))=(4//3R)/(144//7R)=(4)/(3R)xx(7R)/(144)=(7)/(108)`.