Spectrum of Hydrogen Atom

All electromagnetic waves have the same speed (3.0*10^8 m s^-1).
But different types of radiations differ from one another in their wavelengths and therefore, in frequency.

v = c/λ
C = speed = constant
λ = wavelength
v = frequency


The arrangement of different types of electromagnetic radiations in the order of increasing wavelengths (or decreasing frequencies) is known as electromagnetic spectrum.

When white light from sun is passed through a prism, it splits into a series of colour bands know as rainbow of colours: violet, indigo, blue, green, yellow, orange and red (VIBGYOR). This series of colour bands obtained is called a spectrum and in this spectrum of visible light there is continuity of colours, one colour merges into the other without any gap.

We can obtain spectrum of atoms. When the gases of vapour of a chemical substance are heated by electric spark, light is emitted. From such light emitted, the spectrum can be obtained using spectroscope.
It is observed that when radiations emitted by different substances are analysed, the spectrum obtained consists of share well defined lines each corresponding to a definited frequency (or wave length). The spectrum obtained from light emitted by chemical substances is called emission spectrum.

When electromagnetic radiation for example say white light is allowed to pass through a gas or a solution of some salt and the light that comes out is sent through a spectroscope, we obtain a spectrum. In this spectrum some dark lines are observed, in an otherwise continuous spectrum. This indicates that some radiations of specific wavelengths are absorbed by the substance. This spectrum is called absorption spectrum

Spectrum of hydrogen atom

The spectrum of hydrogen atom can be obtained by passing an electric discharge through the hydrogen gas in a discharge tube under low pressure.

It is observed that the spectrum consists of a large number of lines appearing in different regions of wavelengths. Some of the lines are present in visible region while others in ultra-violet and infra-red regions.

In 1885, J.J. Balmer developed a simple relationship among the different wavelengths of the series of visible lines in the hydrogen spectrum.

The relationship developed by Balmer for frequencies observed in hydrogen spe trum is:

1/ λ = v (in cm^-1) = 109677 (1/2² - 1/n²)

Where n is an integer that takes values equal to or greater than 3.
109677 cm^-1 is called Rydberg constant.

The lines in the hydrogen spectrum in various regions of the electromagnetic spectrum are given different names.

Lyman series, Balmer series, paschen series, Brackett series, and Pfund series

Lyman series appears in the ultraviolet region.
Balmer series appear in the visible region.
Other three series appear in the infra red region.

A more general formula for hydrogen spectral lines is

1/ λ = v (in cm^-1) = 109677 (1/nf² - 1/ni²)

ni>nf

ni = the initial level of the electron
nf = the final level of the electron

The above equation is called Rydberg equation.

For lyman series nf = 1
For Balmer series nf = 2
For Paschen series nf = 3
For Brackett series nf = 4
For Pfund series nf = 5

We have to note that above equation is valid for hydrogen spectrum lines only.

Emission of radiation occurs from atoms when electrons in the atom goes into an excited state and then returns to a lower energy state.

For example, if an hydrogen atom goes into an excited state, say the electron goes to fourth energy level and then returns to second energy level, radiation is emitted. The frequency of the emitted radiation can be found out by

1/ λ = v (in cm^-1) = 109677 (1/2² - 1/4²) = 486 nm.

This frequency corresponds to bluish green in visible region.