a
\(\bar v = \frac{1}{\lambda } = {R_H}Z\left( {\frac{1}{{n_1^2}} - \frac{1}{{n_2^2}}} \right)\)

In Balmer series \(n_1=2\) & \(n_2=3,4,5....\)

Last line of the spectrum is called series limit.

Limiting line is the line of shortest wavelength and high enegry when  \({n_2} = \infty \)

\(\therefore \,\bar v = \frac{1}{\lambda } = \frac{{{R_H}}}{{n_1^2}} = \frac{{3.29 \times {{10}^{15}}}}{4}\)

\(= 8.22 \times 10^{14}\,s^{-1}\)