For a hydrogenic ion kinetic energy of electron in its 3rd excited state is found to be 54.4 eV. Then series limit 1λ for Balmer series, for this ion, is

KE=13.6 Z2n2 eV/atom⇒       54.4  =  13.6  ×  Z242⇒       Z2=64for    Balmer   series1λ = RZ2  122−1∞2 for   series    limit=109678  ×  64  14 − 1∞ cm−1=109678  ×16  cm−1