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

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.