Let `v_(1)` be the frequency of series limit of Lyman series, `v_(2)` the frequency of the first line of Lyman series and `v_(3)` the frequency of series limit of Balmer series. Then which of the following is correct ?

Options

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

Answer

A

Explanation

As we know, `v = nlambda`,
`rArr 1/lambda = n/v rArr 1/lambda = R ((1)/(n_(1)^(2))- 1/(n_(2)^(2)))`
`rArr v = Rc ((1)/(n_(1)^(2)) - 1/(n_(2)^(2)))`
`:.`
`v_(2) = Rc((1)/(2^(2)) - 1/(3^(2))) = Rc (1/4 - 1/9)"…"(i)`
`v_(1) = Rc ((1)/(2^(2))) = (Rc)/(4)`
`v_(3) = Rc ((1)/(3^(2))) = (Rc)/(9)`
`rArr v_(1) - v_(3) = Rc (1/4 - 1/9)`
From Eqs. (i) and (ii), we get
`v_(1) - v_(3) = v_(2)`
`rArr v_(1) - v_(2) =v_(3)`