Answer:
The wavelength of the monochromatic light is 486.2 nm.
Explanation:
The illumination of the hydrogen atom by the monochromatic light causes an absorption of energy by its electrons which causes an excitation. After a period, the particle de-excites (decays) losing the absorbed energy and falls back to its initial state releasing the energy in the form of a photon. This photon can be observed as a colored light of the Balmer series.
From Rydberg's expression,
1/λ=−R([tex]\frac{1}{n_{2} ^{2} }[/tex] − [tex]\frac{1}{n_{1} ^{2} }[/tex])
The transition of the electron is from n = 2 to 4, so that;
1/λ = R ([tex]\frac{1}{2^{2} }[/tex] - [tex]\frac{1}{4^{2} }[/tex])
= 1.097 x [tex]10^{7}[/tex] ([tex]\frac{1}{2^{2} }[/tex] - [tex]\frac{1}{4^{2} }[/tex])
1/λ = 2056875
So that,
λ = [tex]\frac{1}{2056875}[/tex]
= 4.8617 x [tex]10^{-7}[/tex] m
The wavelength of the monochromatic light is 486.2 nm.
