If the shortest wavelength in Lyman series of hydrogen atom is A, then the longest wavelength in Paschen series of `He^(+)` is:

Options

A. `(5A)/(9)`
B. `(9A)/(5)`
C. `(36A)/(9)`
D. `(36A)/(7)`

Answer

B

Explanation

For Lyman series (Shortes wavelenght)
`n_(1) = 1, n_(2) = o`
`(1)/(lambda) = Rz^(2) ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))`
`rArr (1)/(A) = 1^(2)R ((1)/(1) - (1)/(oo)) rArr (1)/(A) = R`
Longest wavelenght = `I^(st)` line
`n_(1) = 3,n_(2) = 4`
`(1)/(lambda) = Rz^(2) ((1)/(3^(2)) - (1)/(4^(2))) rArr (1)/(lambda) = (R7)/(36)`
`R =(1)/(A)`
`(1)/(lambda) = ((1)/(A) xx 7)/(36) = (1)/(lambda) = (7)/(36A) rArr lambda = (36A)/(7)`