\(\frac{{\text{1}}}{\lambda }\,\, = \,\,{\text{R}}\,\,\left( {\frac{{\text{1}}}{{{{\text{1}}^{\text{2}}}}}\,\, - \,\,\frac{1}{{{2^2}}}} \right)\,\) પરથી,

\(\,{\left( {{\lambda _{\text{L}}}} \right)_{\max }}\,\, = \,\,\frac{4}{{3\,R}}\)

બામર શ્રેણી ની મહતમ તરંગ લંબાઈ \(\frac{{\text{1}}}{\lambda }\,\, = \,\,R\,\,\left( {\frac{1}{{{2^2}}}\,\, - \,\,\frac{1}{{{3^2}}}} \right)\) પરથી,

\({\left( {{\lambda _B}} \right)_{\max }}\,\, = \,\,\frac{{36}}{{5\,\,R}}\,\,\)

\(\therefore \,\,\frac{{{{\left( {{\lambda _L}} \right)}_{\max }}}}{{{{\left( {{\lambda _B}} \right)}_{\max }}}}\,\, = \,\,\frac{4}{{3\,\,R}}\,\, \times \,\,\,\frac{{5\,\,R}}{{36}}\,\, = \,\,\frac{5}{{27}}\)