An electron makes a transition from orbit n = 4 to the orbit n = 2 of a hydrogen atom. What is the wavelength of the emitted radiations? (R = Rydberg constants)

$\frac{16}{3R}$

The correct answer is Option (4) → $\frac{16}{3R}$

Using Rydberg's formula,

$λ=R_H\left(\frac{1}{{n_f}^2}-\frac{1}{{n_i}^2}\right)$

$⇒\frac{1}{λ}=R_H\left(\frac{1}{4^2}-\frac{1}{2^2}\right)=\frac{3R}{16}$

$λ=\frac{16}{3R}$