\(\frac{h c}{\lambda}=21.76 \times 10^{-19}\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right]\)

Where, \(h=\) Planck's constant \(=6.6 \times 10^{-34} \,Js\)

\(c=\) Speed of light \(=3 \times 10^{8} \,m / s\)

\((n_{1} \text { and } n_{2}\) are integers)

The shortest wavelength present in the Paschen series of the spectral lines is for values \(n_{1}=3\)

and \(n_{2}=\infty\)

\(\frac{h c}{\lambda}=21.76 \times 10^{-19}\left[\frac{1}{(3)^{2}}-\frac{1}{(\infty)^{2}}\right]\)

\(\lambda=\frac{6.6 \times 10^{-34} \times 3 \times 10^{8} \times 9}{21.76 \times 10^{-19}}\)

\(=8.189 \times 10^{-7} \,m\)

\(=818.9 \;nm\)