For single electron species,

\(\frac{1}{λ} = RZ^2 (\frac{1}{n^2_1} - \frac{1}{n^2_2})\)

where, R = Rydberg constant = 1.097×10^{7}×10^{−9}nm^{−1}

= 1.097×10^{−2}nm^{−1}

For Hydrogen atom, Z = Atomic number = 1

For Balmer series, n_{1} = 2 and for longest wavelength in Balmer series, minimum energy transition is to be considered because wavelength is inversely proportional to Energy.

So, n_{2} = 3

∴\(\frac{1}{λ}\)= 1.097×10^{−2}nm^{−1}×1^{2}\((\frac{1}{2^2}-\frac{1}{3^2})\)

⇒ λ = 656nm