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?

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( − )

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

1/λ = R ( - )

    = 1.097 x ( - )

1/λ  = 2056875

So that,

λ =

  = 4.8617 x m

The wavelength of the monochromatic light is 486.2 nm.

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