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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?

1 Answer

7 votes

Answer:

The wavelength of the monochromatic light is 486.2 nm.

Step-by-step 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(
(1)/(n_(2) ^(2) )
(1)/(n_(1) ^(2) ))

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

1/λ = R (
(1)/(2^(2) ) -
(1)/(4^(2) ))

= 1.097 x
10^(7) (
(1)/(2^(2) ) -
(1)/(4^(2) ))

1/λ = 2056875

So that,

λ =
(1)/(2056875)

= 4.8617 x
10^(-7) m

The wavelength of the monochromatic light is 486.2 nm.

User Diana Saunders
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