Question

The longest wavelength emitted in hydrogen atom belonging to Balmer series is ($R$ is Rydberg constant)

• A. $\frac{16}{3R}$
• B. $\frac{36}{7R}$
• C. $\frac{16}{7R}$
• D. $\frac{36}{5R}$

Answer 1

The correct option is D $\frac{36}{5R}$

Longest wavelength corresponds to least energy.
Wavelength of Balmer series, $\frac{1}{\lambda }=R[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$
Therefore $n_1=2$ and $n_2=3$
$\frac{1}{\lambda }=R[\frac{1}{2^2}-\frac{1}{3^2}]$
$\frac{1}{\lambda }=\frac{5R}{36}$
$\Rightarrow \lambda =\frac{36}{5R}$