The ratio of minimum to maximum wavelength of radiation that an electron  can cause in a Bohr's hydrogen atom is:

Energy of radiation that corresponds to the energy difference between two energy levels ${\mathrm{n}}_1 \mathrm{and} {\mathrm{n}}_2$ is given as:

$\begin{array}{l}\mathrm{E}=13.6\left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)\mathrm{eV}\left(\mathrm{numerically}\right)\\ \mathrm{E}\mathrm{is}\mathrm{minimum}\mathrm{when}{\mathrm{n}}_1=1\mathrm{and}{\mathrm{n}}_2=2\\ {\mathrm{E}}_{\min }=1.6\left(\frac{1}{1}-\frac{1}{4}\right)\mathrm{eV}=13.6\times \frac{3}{4}\mathrm{eV}\\ \mathrm{E}\mathrm{is}\mathrm{maximum}\mathrm{when}{\mathrm{n}}_1=1\mathrm{and}{\mathrm{n}}_2=\mathrm{\infty }.\\ \left(\mathrm{The}\mathrm{atom}\mathrm{is}\mathrm{isonized}\mathrm{that}\mathrm{is}\mathrm{known}\mathrm{as}\mathrm{ionization}\mathrm{energy}\right)\\ {\mathrm{E}}_{\max .}=13.6\left(1-\frac{1}{\mathrm{\infty }}\right)=13.6\mathrm{eV}\\ \frac{{\mathrm{E}}_{\min }}{{\mathrm{E}}_{\max }}=\frac{3}{4}\mathrm{or}\frac{\mathrm{hc}/{\mathrm{\lambda }}_{\max }}{\mathrm{hc}/{\mathrm{\lambda }}_{\min }}=\frac{3}{4}\\ \frac{{\mathrm{\lambda }}_{\min }}{{\mathrm{\lambda }}_{\max }}=\frac{3}{4}\end{array}$