Explanation

(b) For Balmer series, $n_{f}$ =2 and $n_{i}$=3,4,5,….
Frequency, of 1st spectral line of Balmer series
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ f$ $=$ $RZ^{2}\ c\left( \frac{1}{2^{2}} - \frac{1}{3^{2}} \right)$
or $\ \ \ \ \ \ \ \ \ f = RZ^{2}\ c \times \frac{5}{36}$ …(i)
Frequency, of 2nd spectral line of Balmer series
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ f’\ =$ $RZ^{2}\ c\left( \frac{1}{2^{2}} - \frac{1}{4^{2}} \right)$
or $\ \ \ \ \ \ \ \ f' = RZ^{2}\ c \times \frac{3}{16}$ ….(ii)
Form eqs. (i) and (ii), we have
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{f}{f'}$ $= \frac{20}{27}$
$\therefore\ \ f^{'} = \frac{27}{20}\ f = 1.35\ f$