$\frac{1}{\lambda } = R(\frac{1}{{{{n'}^2}}} - \frac{1}{{{n^2}}}) = \frac{1}{{100}}(\frac{1}{{16}} - \frac{1}{{49}})$$ = \frac{1}{{100}}(\frac{{33}}{{16 \times 49}}) \Rightarrow \lambda  = \frac{{4900 \times 16}}{{33}} \simeq 2376nm$