Let`lambda_(P)` and `lambda_(L)` be the longest wavelengths observed in the Paschen and Lyman series respectively. Choose the correct option

Options

A. `4 lt (lambda_(P))/(lambda_(L))lt 6`
B. `7 lt (lambda_(P))/(lambda_(L))lt 8`
C. `15 lt (lambda_(P))/(lambda_(L))lt 16`
D. `30 lt (lambda_(P))/(lambda_(L))lt 32`

Answer

C

Explanation

As we know, wavelength for Paschen-series.
`(1)/(lambda_(p))=R[(1)/(3^(2))-(1)/(n_(p)^(2))],n_(p)=4,5,6`
and wavelength for Lyman-series,
`(1)/(lambda_(L))=R[1-(1)/(n_(L)^(2))], n_(L)=2, 3, 4...`
Hence, `lambda_(p)` for `n_(p)=4`
`(1)/(lambda_(p))=R[1/9-1/16],=(7R)/(9xx16)` ...(i)
and `lambda_(L)` for `n_(L)=2`
`(1)/(lambda_(L))=R[1-1/4]=(3R)/(4)` ...(iii)
From Eq. (i) and (ii), we get
`(lambda_(p))/(lambda_(L))=(3R//4)/(7R//9xx16)=15.42`
So, `15 lt (lambda_(p))/(lambda_(L))lt16`
Hence, the correct option is (c).