Question

A sample tube consisted of atomic hydrogen in their ground state. A student illuminated the atoms with monochromatic light, that is, light of a single wavelength. If only two separate emission lines in the visible region are observed, what is the wavelength (or wavelengths) of the incident radiation?

Answer 1

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($\frac{1}{n_{2} ^{2} }$ − $\frac{1}{n_{1} ^{2} }$)

The transition of the electron is from n = 2 to 4, so that;

1/λ = R ($\frac{1}{2^{2} }$ - $\frac{1}{4^{2} }$)

    = 1.097 x $10^{7}$ ($\frac{1}{2^{2} }$ - $\frac{1}{4^{2} }$)

1/λ  = 2056875

So that,

λ = $\frac{1}{2056875}$

  = 4.8617 x $10^{-7}$ m

The wavelength of the monochromatic light is 486.2 nm.