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

Options

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

Answer

D

Explanation

For first line of Paschen series `n_(1)=1 and n_(2)=2`.
`therefore (1)/(lamda_(1))=R((1)/(1^(2))-(1)/(2^(2)))=R(1-(1)/(4))=(3R)/(4)`
For first line of Paschen series `n_(1)=3 and n_(2)=4`
`therefore (1)/(lamda_(2))=R((1)/(3^(2))-(1)/(4^(2)))=R((1)/(9)-(1)/(16))=(7R)/(144)`
`therefore (lamda_(1))/(lamda_(2))=(7R)/(144)xx(4)/(3R)=(7)/(108)`