The shortest wavelength present in the Paschen series of spectral lines is _______. $(\mathrm{R} = 1.097\times {10}^7 {\mathrm{m}}^{-1})$

The wavelength for Paschen series, $\frac{1}{\lambda }=R\left[\frac{1}{3^2}-\frac{1}{n^2}\right]$ 

For shortest wavelength $n=\infty$

$$\begin{gathered} \therefore \frac{1}{\lambda }=R\left[\frac{1}{9}-\frac{1}{{\infty }^2}\right]=\frac{R}{9} \\ \Rightarrow \lambda =\frac{9}{R}=\frac{9}{1.097\times {10}^7} \\ = 8.20\times {10}^{-7} \mathrm{m} \\ = 820 \mathrm{nm} \end{gathered}$$