For Balmer series, $n_f$ =2 and $n_i$=3,4,5,....

Frequency, of 1st spectral line of Balmer series

$f$ $=$ $R{Z}^2 c\left(\frac{1}{2^2}-\frac{1}{3^2}\right)$

or $f=R{Z}^2 c\times \frac{5}{36}$ ...(i)

Frequency, of 2nd spectral line of Balmer series

$f’ =$ $R{Z}^2 c\left(\frac{1}{2^2}-\frac{1}{4^2}\right)$

or $f\prime =R{Z}^2 c\times \frac{3}{16}$ ....(ii)

Form eqs. (i) and (ii), we have

$\frac{f}{f\prime }$ $=\frac{20}{27}$

$\therefore f^{\prime }=\frac{27}{20} f=1.35 f$