Correct Answer is: (a) ν1 - ν2 = ν3
Series limit means the shortest possible wavelength (maximum photon energy), and first line means the longest possible wavelength (minimum photon energy) in the series.
ν = c [1/n2 - 1/m2], where c = constant.
For series limit of the Lyman series, n = 1, m = ∞, ν1 = c.
For first line of the Lyman series, n = 1, m = 2, ν2 = 3c/4 .
For series limit of the Balmer series, n = 2, m ∞, ν3 = c/4.
∴ ν1 - ν2 = ν3.