`v_(1)` is the frequency of the series limit of Lyman series, `v_(2)` is te frequency of the first line of Lyman series and `v_(3)` is the frequency of the series limit of the Balmer series. Then

Options

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

Answer

A

Explanation

For Lyman series
`v=RC[(1)/(1^(2))-(1)/(n^(2))]`
where `n=2,3,4, . . . . `
For the series limit of Lyman series
`n=oo`
`:.v_(1)=RC[(1)/(1^(2))-(1)/(oo^(2))]=RC` . . . (i)
For the first line of Lyman series, `n=2`
`:.v_(2)=RC[(1)/(1^(2))-(1)/(2^(2))]=3/4RC` . . . (ii)
For Balmer series
`v=RC[(1)/(2^(2))-(1)/(n^(2))]`
where `n=3,4,5 . . . .`
For the series limit of Balmer series `n=oo`
`:.v_(3)=RC[(1)/(2^(2))-(1)/(oo^(2))]=(RC)/(4)` . . . (iii)
From equations (i), (ii) and (iii), we get
`v_(1)=v_(2)+v_(3)` or `v_(1)-v_(2)=v_(3)`