When an electron jumps from outer orbits to the second orbit, the series is called Balmer series. Using Eqn. (1.8), the wavelength limit for the Balmer series can be found by calculating the wavelength of the radiation due to the transition of electron from the infinite orbit to the second orbit.

\lambda =\frac{12,400}{E_{2}-E_{1} }   (1.8)

Wavelength of the Balmer series limit      =\frac{12,400}{E_{\infty }-E_{2} }

Energy of the electron at the infinite orbit, E_{\infty }=\frac{ -13.6 }{\infty ^{2}}=0

Energy of the electron at the second orbit, E_{2}=\frac{-13.6}{2^{2} }=-3.4

Therefore, the wavelength limit         =\frac{12,400}{E_{\infty }-E_{2}} =\frac{12,400}{3.4}=3647A.U.