question_answer

What is the shortest wavelength present in the Paschen series of spectral lines?

Answer:

\[\lambda =820.4nm\] For shortest wavelength of Paschen series, \[{{n}_{1}}=3,{{n}_{2}}=\infty \] \[\therefore \]      \[\frac{1}{\lambda }=R\left[ \frac{1}{{{n}_{2}}}-\frac{1}{n_{2}^{2}} \right]=R\left[ \frac{1}{9}-\frac{1}{\infty } \right]=\frac{R}{9}\] or         \[\lambda =\frac{9}{R}=\frac{9}{1.097\times {{10}^{7}}{{m}^{-1}}}=820.4\,\,\text{nm}\]