In 1913 Niels Bohr established a model for the atom now known as the Bohr model. His model described the atom comprising of a central nucleus surrounded by electrons in spherical orbits of different energies. At the same time he also derived a relationship that defined the relationship between the spectral emission / absorption wavelength and the energy level in his atomic model. Using this relationship Bohr, was able to calculate the energy levels of the hydrogen atom and thus the atomic emission / absorption lines, in agreement with experimental results.

In .....Planck made the assumption that electrons can exist only in specific quantized energy levels. These energies are described by the principle quantum number n of the electron, where n is an integer number (1, 2, 3, ...). Each value of n corresponds to a permitted value of the orbital radius. Electrons may only exist in these states and only transit between these specific states. Planck however found this an absurd idea and laughed away at it. But, then in the golden year of 1905, Albert Einstein verified Max Planck’s absurd idea by explaining the photoelectric effect.

© 2011 Karl Gaff. All Rights Reserved
The Bohr Atom & Optical Spectra
The visible spectrum of light from hydrogen displays four wavelengths, 410 nm, 434 nm, 486 nm, and 656 nm. These wavelengths correspond to emissions of photons by the transitioning of electrons from excited states to the n = 2 energy level.
In the Hydrogen atom, the set of transitions from the principal quantum number n > / = 3 to n = 2 is called the Balmer series. The spectral components of the Balmer series include Balmer-alpha or H-alpha (n = 3 to n = 2) (656.3 nm) (red line), Balmer-beta or H-beta (n = 4 to n = 2) (486.1 nm) (Blue-green line), and from here on, the higher transitions from (n = infinity to n = 2) emit shades of violet.
Absorption spectrum of hydrogen
Emission spectrum of hydrogen

The Balmer equation an empiracal equation discovered by Johann Balmer in 1885 predicts the four visible spectral lines of hydrogen with a high degree of precision. The Balmer equation is stated as









The Balmer series is one of 6 different named series describing spectral line emissions in the hydrogen atom.
The second set of transitions in the hydrogen atom is called the Lyman series whose spectral components are called Lyman-alpha (), Lyman-beta (), etc. Balmer's equation was the inspiration of Johannes Rydberg who in 1888 derived the equation which describes Balmers equation but in a
generalized form to work out all the spectral lines in the hydrogen atom. This breakthrough led physicists to find the Lyman, Paschen, and Brackett series of absorption / emission lines of the hydrogen atom found outside the visible spectrum. The Rydberg equation is stated as






Letting n=3 we can calculate the wavelength of the hydrogen-alpha line:




Letting n=4 we can calculate the wavelength of the hydrogen-beta line:




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Angelo Secchi of the Vatican Observatory began recording and analysing the spectra of stars, accumulating over 4,000 spectrograms. He discovered that stars could be classified into a number of distinct types and subtypes, which could be distinguished by their spectral types (ie. by the number and strength of absorption lines in their spectra). Three groups emerged. Blue and White stars, yellow stars, orange and red stars. It was later found that the spectral types of the stars were related to their surface temperatures. Particular absorption lines can be observed through a certain temperature range because it is only in this temperature range that the atomic energy levels involved can be populated. In the late 1890’s, the Secchi classification scheme began to be replaced by the Harvard spectral classification scheme.

In 1868, Sir Norman Lockyer observed a peculiar set of yellow emission lines in the solar spectrum which he concluded must be due to some other unknown element, which he named Helium from the Greek word helios meaning Sun.

When the British astronomer William Huggins peered through the telescope at the Cat's Eye nebula, he was astonished to find isolated emission lines. It was later discovered in the 1920s that the emission lines were due to ionised oxygen atoms. Nebulae are extremely rarefied, to a much higher degree than the hardest vacuum ever produced here on Earth. In these conditions, atoms behave quite differently and lines can form which are suppressed at normal densities. These lines are known as forbidden lines, and are the most intense lines in most nebular spectra.


Thirty four years later, in 1849, Leon Foucault studied the emission spectra of Sodium. Ten years later, the researchers, Gustav Kirchoff and Robert Bunsen identified the sodium emission lines buried in the solar spectrum. This marked a major advancement in spectroscopy. They then realised that each and every element in the periodic table of elements bears it’s own unique spectral finger print that is truly unique to that element and is insolubly keyed to that element as the lines of your finger prints are keyed to you. Kirchoff formalized three laws of spectroscopy to describe the spectral
compsosition of light emitted by incandescent objects.

In the year 1666, Isaac Newton held a prism up to an aperture through which light from our nearest star shone through. In doing so, Newton dispersed the star light into a band of colours from red to violet in what is called the solar spectrum, projecting it onto a nearby screen, before cohering the spectrum of colours back into white light by means of a lens and a second prism. However, Newton remained unaware as to what vital information actually lay hidden in the spectra he had just produced before him.
A French philosopher called Auguste Comte, in the year 1835 published a book entitled ‘Positive Philosphy’. In this book he wrote of the stars, “We see how we may determine their forms, their distances, their bulk, their motions but we can never know anything of their chemical or mineralogical structure”. Yet, 33 years earlier, in 1802, William Hyde Wollaston, directed sun light through a prism and observed fine dark spectral lines superimposed on the spectrum where the light had been absorbed at discreet wavelengths.

1] A solid object, whose internal energy is raised to a sufficient level, emits a continuous spectrum of light.

2] A tenuous gas, whose temperature is raised to a sufficient level, emits spectral lines that occur at discreet wavelengths, depending on what elements the gas is composed of.

3] A solid object with a sufficient amount of internal energy surrounded by a cool tenuous gas emits light with an almost continuous spectrum which has gaps at discrete wavelengths depending on the energy levels of the atoms in the gas.

Appearing very similar to a barcode, each dark line in a spectrum indicates a wavelength absorbed whilst each bright line indicates an emission wavelength. Light passing through a relatively cool gas, such as the
temperature minimum region of the Sun for example, produces an absorption spectrum, in this case called the Fraunhofer spectrum.

Kirchhoff did not know about the existence of energy levels in atoms. The existence of discrete spectral lines was later explained by the Bohr model of the atom, which helped lead to quantum mechanics.

These dark lines were then studied in detail by a poor glass-polisher’s apprentice named Josef von Fraunhofer, who in 1814 had catalogued 475 of these dark lines in the solar spectrum. While Franhofer precisely measured the wavelengths at which these lines occurred along the spectrum, he made a startling discovery! In the yellow region of the spectrum, he realised that a wavelength
measurement he had just made, corresponded with the wavelength of the yellow light emitted when grains of sodium chloride, commonly known as table salt, are sprinkled in a flame, proving Auguste Comte wrong. And in doing so, he discovered that these dark lines were in fact spectral absorption lines. With the identification of this sodium line, the science of spectroscopy was born.
Cataloging these spectral lines, he grouped them into sets, assigning each set with a letter of the alphabet. At 759.4 nm and 686.7 nm, Fraunhofer assigned these lines with the letters A and B respectively, whose origins were later discovered to come from Earth’s atmospheric oxygen, assiging the line at 656.3 nm also in the red the letter C, this is made from hydrogen, he assigned the sodium yellow lines the letter D, the green line with the letter E which is iron, the blue line F originating from hydrogen once again, violet G which are both iron and calcium…

The Balmer lines appear in the spectra from a variety of astrophysical objects due to the abundance of hydrogen in the cosmos. They play an integral role in the astronomers tool box as they can be used to determine radial velocities due to doppler shifting of the Balmer lines. This has important uses all over astronomy, from detecting binary stars, exoplanets, compact objects such as neutron stars and black holes (by the motion of hydrogen in accretion disks around them), identifying groups of objects with similar motions and presumably origins (moving groups, star clusters, galaxy clusters, and debris from collisions), determining distances (actually redshifts) of galaxies or quasars, and identifying unfamiliar objects by analysis of their spectrum.

Balmer lines can appear as absorption or emission lines in a spectrum, depending on the nature of the object observed. In stars, the Balmer lines are usually seen in absorption, and they are "strongest" in stars with a surface temperature of about 10,000 kelvin (spectral type A).

In the spectra of most spiral and irregular galaxies, active galactic nuclei (AGN), H II regions and planetary nebulae, the Balmer lines are emission lines.

In stellar spectra, the H-epsilon line (transition n = 7 to n = 2) is often mixed in with another absorption line produced by ionized calcium known by astronomers as "H" (the original designation given by Fraunhofer). H-epsilon's wavelength is quite close to CaH at 396.847 nm and cannot be resolved in low resolution spectra. The H-zeta line (transition n = 8 to n = 2) is similarly mixed in with a neutral helium line seen in hot stars.

Since it takes nearly as much energy to excite the hydrogen atom's electron from n = 1 to n = 3 as it does to ionize the hydrogen atom, the probability of the electron being excited to n = 3 without being removed from the atom is very small. This means the vast majority of atoms in nebulae are in there ionized state, but not them all, according to Maxwell-boltzmann distribution of energies.

Instead, after being ionized, the electron and proton recombine to form a new hydrogen atom. In the new atom, the electron may begin in any energy level, and subsequently cascades to the ground state (n = 1), emitting photons with each transition. Approximately half the time, this cascade will include the n = 3 to n = 2 transition and the atom will emit H-alpha light. Therefore, the H-alpha line occurs where hydrogen is being ionized.

Image captured by: Greg Parker
and Noel Carponi