d
From energy level diagram, using \(\Delta E=\frac{h c}{\lambda}\)

For wavelength \(\lambda_{1} \Delta E=-E-(-2 E)=\frac{h c}{\lambda_{1}}\)

\(\therefore \quad \lambda_{1}=\frac{h c}{E}\)

For wavelength \(\lambda_{2} \Delta E=-E-\left(-\frac{4 E}{3}\right)=\frac{h c}{\lambda_{2}}\)

\(\therefore \quad {\lambda _2} = \frac{{hc}}{{\left( {\frac{E}{3}} \right)}}\) \(\therefore r = \frac{{{\lambda _1}}}{{{\lambda _2}}} = \frac{1}{3}\)