\({n_1} = 2,\,\,\,\,{n_2} = 3\,\,\,\,\,\,\,\)

\(\frac{1}{\lambda }\,\, = \,\,R{(1)^2}\left[ {\frac{1}{4} - \frac{1}{9}} \right]\,\,\,\, \Rightarrow \,\,\,\frac{1}{\lambda } = R\left[ {\frac{{9 - 4}}{{36}}} \right]\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\frac{1}{\lambda } = R\left[ {\frac{5}{{36}}} \right]\,\,\,\,\)

\(\lambda  = \frac{{36}}{{5R}}\,\,\,\therefore \,\,\,\,\,\,\lambda  = \frac{{36}}{5} \times \frac{1}{R}\,\,\,\, = \,\,\frac{{36}}{5} \times 9.12 \times {10^{ - 6}}cm\,\,\,\, = \,\,65.66 \times {10^{ - 6}}\,cm\)

\(\{ \because \,{\mkern 1mu} {\mkern 1mu} 1\,\mathop A\limits^o {\mkern 1mu} {\mkern 1mu}  = {\mkern 1mu} {\mkern 1mu} {10^{ - 8}}{\mkern 1mu} cm,{\mkern 1mu} {\mkern 1mu} \,\,\,\therefore {\mkern 1mu} {\mkern 1mu} 1\,{\mkern 1mu} cm{\mkern 1mu} {\mkern 1mu}  = {\mkern 1mu} {\mkern 1mu} {10^8}\,\mathop A\limits^o \} {\mkern 1mu} \)

\( = 5.66 \times {10^{ - 6}} \times {10^8}\,\mathop A\limits^o {\mkern 1mu} {\mkern 1mu}  = {\mkern 1mu} {\mkern 1mu} 65.66 \times {10^2}\,\mathop A\limits^o {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu}  = 6566\,\mathop A\limits^o \)