Explanation:
: In the Balmer series, the energy gap is very less between $\mathrm{n}=2$ to $\mathrm{n}=3$.
So, the wavelength high in nature.
Given that, Rydberg constant $=1.097 \times 10^7 \mathrm{~m}^{-1}$
Using the following Formula-
$\bar{v}=1.097 \times 10^7\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right)$
or $\quad \bar{v}=1.097 \times 10^7\left(\frac{1}{4}-\frac{1}{9}\right)$
or $\quad \bar{v}=1.097 \times 10^7 \times \frac{5}{36}$
or $\quad \bar{v}=0.1523 \times 10^7 \mathrm{~m}^{-1}$
We know that,
$\lambda=\frac{1}{\bar{v}}$
$\begin{aligned}
\lambda & =\frac{1}{0.1523 \times 10^7 \mathrm{~m}^{-1}} \\
\lambda & =6.56 \times 10^{-7} \mathrm{~m} \\
\text { or } \quad \lambda & =656 \mathrm{~nm}
\end{aligned}$
