Assuming f & to be the frequency of the electromagnetic wave...

For Balmer series, ${n}_{f}$ =2 and ${n}_{i}$=3,4,5,....

Frequency, of 1st spectral line of Balmer series

$f=RZ^{2}c \left(\dfrac{1}{{2}^{2}} - \dfrac{1}{{3}^{2}}\right)<br /><br />or$f = RZ^{2}c $\times \dfrac{5}{36} ...(i)<br /><br />Frequency,$ of 2nd spectral line of Balmer series

f’ =RZ^{2}c \left(\dfrac{1}{{2}^{2}} - \dfrac{1}{{4}^{2}}\right)$<br /><br />or$f′ = RZ^{2}c \times \dfrac{3}{16}$....(ii)<br /><br />Form eqs. (i) and (ii), we have<br /><br />$\dfrac{f}{f′}= \dfrac{20}{27}$<br /><br />$∴ f^{′} = \dfrac{27}{20}f = 1.35f