Question

$\frac{1}{\lambda} = RZ^{2}\left( \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right) \Rightarrow \frac{1}{1028 \times 10^{- 10}} = 1.09 \times 10^{7} \times 1^{2}\left( \frac{1}{1^{2}} - \frac{1}{n^{2}} \right)$

$\therefore n = 3$

$\lambda_{1} = 1028\ \overset{o}{A} $$${\frac{\lambda_{2}}{\lambda_{1}} = \frac{\left( \frac{1}{1^{2}} - \frac{1}{3^{2}} \right)}{\left( \frac{1}{2^{2}} - \frac{1}{3^{2}} \right)} \Rightarrow \lambda_{2} = 6579.2\overset{o}{A} }{\frac{\lambda_{3}}{\lambda_{1}} = \frac{\left( \frac{1}{1^{2}} - \frac{1}{3^{2}} \right)}{\left( \frac{1}{1^{2}} - \frac{1}{2^{2}} \right)} \Rightarrow \lambda_{3} = 1218.4\overset{o}{A}}$$