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

Answer

A

Explanation

Series limit means the shortest possible wavelength (maximum photon energy) and first line means the largest possible wavelength (minimum photon energy) in the series.
`v = C [(1)/(n^(2)) - (1)/(m^(2))]` (where `C` is a constant)
For series limit of Lyman series :
`n = 1, m = oo implies v_(1) = C`
For first line Lyman series:
`n = 1, m = oo implies v_(2) = 3 C//4`
For series limit of Balmer series :
`n = 2, m = oo implies v_(3) = C//4`.