Let `v_(1)` be the frequency of the series limit of the lyman series `v_(2)` be the frequency of the first line of th elyman series and `v_(3)` be the frequency of the series limit of the Balmer series

Options

A. `nu_(1)` - `nu_(2)` = `nu_(3)`
B. `nu_(2)` - `nu_(1)` = `nu_(3)`
C. `nu_(2)` = `1/2( nu_(1) - nu_(3))`
D. `nu_(1)` + `nu_(2)` = `nu_(3)`

Answer

`nu_(1)` - `nu_(2)` = `nu_(3)`

Explanation

Lyman series limit `(n_(1) = 1,,n_(2)= oo)`
`v_(1) = RZ^(2)((1)/(1^(2)) - (1)/(oo^(2))) = RZ^(2) = R(Z = 1)`
First line of lyman `(n_(1) = 1,,n_(2)= 2)`
`v_(2) = R((1)/(1^(2)) - (1)/(2^(2))) = (3)/(4)R = (3)/(4)(v_(1)) (v_(1) = R)`
Balmer series limit
`(n_(1) = 1,,n_(2)= oo)`
`V_(3) = R((1)/(2^(2)) - (1)/(oo^(2))) = (R)/(4) = (v_(1))/(4)`
`v_(3) = (v_(1) - v_(2)) = (v_(1) - (3)/(4) v_(1))= (v_(1))/(4)`
`:. (v_(1) - v_(2)) = v_(3)`