a
\({{\text{E}}_{\text{i}}}\,\, - \,\,{E_k}\,\, = \,\,\frac{{m{e^4}\,\,{Z^2}}}{{8{ \in _0}^2{h^2}}}\,\,\left( {\frac{1}{{{n_k}^2}}\,\, - \,\,\frac{1}{{{n_i}^2}}} \right)\,\)  પરથી, જ્યાં \({n_i}\,\, > \,\,{n_k}\)

અહીં \(\Delta E\,\, \propto \,\,{Z^2}\)  (\(\because\) \(n_k = 1\) અને \(n_i = 2\) અચળ છે.)

\(\therefore\) \(\,\frac{{hc}}{\lambda }\,\, \propto \,\,{Z^2}\,\,\)

\(\therefore\) \(\lambda {Z^2} =\) અચળ

\(\therefore\) \({\lambda _1}\,\,{\left( 1 \right)^2}\,\, = \,\,{\lambda _2}\,\,{\left( 1 \right)^2}\,\, = \,\,{\lambda _3}\,\,{\left( 2 \right)^2}\,\, = \,\,{\lambda _4}\,\,{\left( 3 \right)^2}\,\)

\(\therefore\) \({\lambda _1}\,\, = \,\,{\lambda _2}\,\, = \,\,4{\lambda _3}\,\, = \,\,9{\lambda _4}\)