The wavelength of the first spectral line of the Lyman series is `lambda` then the wavelength of the first spectral line of the Paschen series is .........`lambda`

Options

A. `(108)/(7)`
B. `(27)/(5)`
C. `(7)/(108)`
D. `(5)/(7)`

Answer

A

Explanation

The wavelength of the first spectral line of the Lyman series
`(1)/(lambda_(L))=R[(1)/(1^(2))-(1)/(n^(2))]=R[(1)/(1^(2))-(1)/(2^(2))]=R[(1)/(1)-(1)/(4)]=R[(3)/(4)]`
`:. lambda_(L)=(4)/(3R).....(1)`
The wavelength of the first spectral line of the Paschen series
`(1)/(lambda_(P))=R[(1)/(3^(2))-(1)/(4^(2))]= R[(1)/(9)-(1)/(16)]=R[(7)/(144)]`
`:. lambda_(p)=(144)/(7R).....(2)`
`:. (lambda_(P))/(lambda_(L))=(144)/(7R)xx(3R)/(4)=(108)/(7) :. lambda_(P)=(108)/(7)xx lambda`