The first member of the Paschen series in hydrogen spectrum is of wavelength 18,800 Å. The short wavelength limit of Paschen series is:

 First member of Paschen series mean it's ${\lambda }_{max}=\frac{144}{7R}$

Short wavelength of Paschen series means ${\lambda }_{min}=\frac{9}{R}$

Hence $$\begin{gathered} \frac{{\lambda }_{max}}{{\lambda }_{min}}=\frac{16}{7} \\ \Rightarrow {\lambda }_{min}=\frac{7}{16}\times {\lambda }_{max}=\frac{7}{16}\times 18,800=8225\stackrel{°}{A} \end{gathered}$$