![Visible spectrum of hydrogen](https://upload.wikimedia.org/wikipedia/commons/2/21/Visible_spectrum_of_hydrogen.jpg)
The Balmer series, or Balmer lines in
atomic physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...
, is one of a set of
six named series describing the
spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to ident ...
emissions of the
hydrogen atom
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen cons ...
. The Balmer series is calculated using the Balmer formula, an
empirical
Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and ...
equation discovered by
Johann Balmer
Johann Jakob Balmer (1 May 1825 – 12 March 1898) was a Swiss mathematician best known for his work in physics, the Balmer series of hydrogen atom.
Biography
Balmer was born in Lausen, Switzerland, the son of a chief justice also named Johan ...
in 1885.
The visible
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors ...
of
light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 t ...
from
hydrogen
Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...
displays four
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
s, 410
nm, 434 nm, 486 nm, and 656 nm, that correspond to emissions of
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alwa ...
s by
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have n ...
s in excited states transitioning to the quantum level described by the
principal quantum number
In quantum mechanics, the principal quantum number (symbolized ''n'') is one of four quantum numbers assigned to each electron in an atom to describe that electron's state. Its values are natural numbers (from 1) making it a discrete variable.
A ...
''n'' equals 2.
There are several prominent
ultraviolet
Ultraviolet (UV) is a form of electromagnetic radiation with wavelength from 10 nm (with a corresponding frequency around 30 PHz) to 400 nm (750 THz), shorter than that of visible light, but longer than X-rays. UV radiation ...
Balmer lines with wavelengths shorter than 400 nm. The number of these lines is an infinite continuum as it approaches a limit of 364.5 nm in the ultraviolet.
After Balmer's discovery, five other
hydrogen spectral series were discovered, corresponding to electrons transitioning to values of ''n'' other than two .
Overview
![Bohr atom model](https://upload.wikimedia.org/wikipedia/commons/9/93/Bohr_atom_model.svg)
The Balmer series is characterized by the
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have n ...
transitioning from ''n'' ≥ 3 to ''n'' = 2, where ''n'' refers to the
radial quantum number or
principal quantum number
In quantum mechanics, the principal quantum number (symbolized ''n'') is one of four quantum numbers assigned to each electron in an atom to describe that electron's state. Its values are natural numbers (from 1) making it a discrete variable.
A ...
of the electron. The transitions are named sequentially by Greek letter: ''n'' = 3 to ''n'' = 2 is called H-α, 4 to 2 is H-β, 5 to 2 is H-γ, and 6 to 2 is H-δ. As the first spectral lines associated with this series are located in the visible part of the
electromagnetic spectrum
The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies.
The electromagnetic spectrum covers electromagnetic waves with frequencies ranging fro ...
, these lines are historically referred to as "H-alpha", "H-beta", "H-gamma", and so on, where H is the element hydrogen.
:
Although physicists were aware of atomic emissions before 1885, they lacked a tool to accurately predict where the spectral lines should appear. The Balmer equation predicts the four visible spectral lines of hydrogen with high accuracy. Balmer's equation inspired the
Rydberg equation
In atomic physics, the Rydberg formula calculates the wavelengths of a spectral line in many chemical elements. The formula was primarily presented as a generalization of the Balmer series for all atomic electron transitions of hydrogen. It was ...
as a generalization of it, and this in turn led physicists to find the
Lyman,
Paschen, and
Brackett series
The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are due to the electron making transitions between two energy levels in an ...
, which predicted other spectral lines of hydrogen found outside the
visible spectrum
The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called '' visible light'' or simply light. A typical human eye will respond to ...
.
The red
H-alpha
H-alpha (Hα) is a specific deep-red visible spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared wit ...
spectral line of the Balmer series of atomic hydrogen, which is the transition from the shell ''n'' = 3 to the shell ''n'' = 2, is one of the conspicuous colours of the
universe
The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the univers ...
. It contributes a bright red line to the spectra of
emission or ionisation nebula, like the
Orion Nebula
The Orion Nebula (also known as Messier 42, M42, or NGC 1976) is a diffuse nebula situated in the Milky Way, being south of Orion's Belt in the constellation of Orion. It is one of the brightest nebulae and is visible to the naked eye in the ni ...
, which are often
H II region
An H II region or HII region is a region of interstellar atomic hydrogen that is ionized. It is typically in a molecular cloud of partially ionized gas in which star formation has recently taken place, with a size ranging from one to hundreds ...
s found in star forming regions. In true-colour pictures, these nebula have a reddish-pink colour from the combination of visible Balmer lines that hydrogen emits.
Later, it was discovered that when the Balmer series lines of the hydrogen spectrum were examined at very high resolution, they were closely spaced doublets. This splitting is called
fine structure
In atomic physics, the fine structure describes the splitting of the spectral lines of atoms due to electron spin and relativistic corrections to the non-relativistic Schrödinger equation. It was first measured precisely for the hydrogen atom ...
. It was also found that excited electrons from shells with ''n'' greater than 6 could jump to the ''n'' = 2 shell, emitting shades of ultraviolet when doing so.
Balmer's formula
Balmer noticed that a single wavelength had a relation to every line in the hydrogen spectrum that was in the visible
light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 t ...
region. That wavelength was . When any integer higher than 2 was squared and then divided by itself squared minus 4, then that number multiplied by (see equation below) gave the wavelength of another line in the hydrogen spectrum. By this formula, he was able to show that some measurements of lines made in his time by
spectroscopy
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter ...
were slightly inaccurate and his formula predicted lines that were later found although had not yet been observed. His number also proved to be the limit of the series.
The Balmer equation could be used to find the
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
of the absorption/emission lines and was originally presented as follows (save for a notation change to give Balmer's constant as ''B''):
Where
*''λ'' is the wavelength.
*''B'' is a constant with the value of or .
*''m'' is equal to 2
*''n'' is an integer such that ''n'' > ''m''.
In 1888 the physicist
Johannes Rydberg
Johannes (Janne) Robert Rydberg (; 8 November 1854 – 28 December 1919) was a Swedish physicist mainly known for devising the Rydberg formula, in 1888, which is used to describe the wavelengths of photons (of visible light and other electro ...
generalized the Balmer equation for all transitions of hydrogen. The equation commonly used to calculate the Balmer series is a specific example of the
Rydberg formula
In atomic physics, the Rydberg formula calculates the wavelengths of a spectral line in many chemical elements. The formula was primarily presented as a generalization of the Balmer series for all atomic electron transitions of hydrogen. It wa ...
and follows as a simple reciprocal mathematical rearrangement of the formula above (conventionally using a notation of m for n as the single integral constant needed):
where ''λ'' is the wavelength of the absorbed/emitted light and ''R''
H is the
Rydberg constant
In spectroscopy, the Rydberg constant, symbol R_\infty for
heavy atoms or R_\text for hydrogen, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to the electromagnetic spectra of an atom. The constant first aro ...
for hydrogen. The Rydberg constant is seen to be equal to in Balmer's formula, and this value, for an infinitely heavy nucleus, is = .
Role in astronomy
The Balmer series is particularly useful in
astronomy
Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...
because the Balmer lines appear in numerous stellar objects due to the abundance of hydrogen in the
universe
The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the univers ...
, and therefore are commonly seen and relatively strong compared to lines from other elements.
The
spectral classification
In astronomy, stellar classification is the classification of stars based on their spectral characteristics. Electromagnetic radiation from the star is analyzed by splitting it with a prism or diffraction grating into a spectrum exhibiting th ...
of stars, which is primarily a determination of surface temperature, is based on the relative strength of spectral lines, and the Balmer series in particular is very important. Other characteristics of a star that can be determined by close analysis of its spectrum include
surface gravity
The surface gravity, ''g'', of an astronomical object is the gravitational acceleration experienced at its surface at the equator, including the effects of rotation. The surface gravity may be thought of as the acceleration due to gravity experien ...
(related to physical size) and composition.
Because the Balmer lines are commonly seen in the spectra of various objects, they are often used to determine
radial velocities due to
doppler shift
The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who ...
ing of the Balmer lines. This has important uses all over astronomy, from detecting
binary star
A binary star is a system of two stars that are gravitationally bound to and in orbit around each other. Binary stars in the night sky that are seen as a single object to the naked eye are often resolved using a telescope as separate stars, in ...
s,
exoplanet
An exoplanet or extrasolar planet is a planet outside the Solar System. The first possible evidence of an exoplanet was noted in 1917 but was not recognized as such. The first confirmation of detection occurred in 1992. A different planet, init ...
s, compact objects such as
neutron star
A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses, possibly more if the star was especially metal-rich. Except for black holes and some hypothetical objects (e.g. w ...
s and
black hole
A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can def ...
s (by the motion of hydrogen in
accretion disk
An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is typically a star. Friction, uneven irradiance, magnetohydrodynamic effects, and other ...
s around them), identifying groups of objects with similar motions and presumably origins (
moving groups,
star cluster
Star clusters are large groups of stars. Two main types of star clusters can be distinguished: globular clusters are tight groups of ten thousand to millions of old stars which are gravitationally bound, while open clusters are more loosely cl ...
s,
galaxy cluster
A galaxy cluster, or a cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxies that are bound together by gravity, with typical masses ranging from 1014 to 1015 solar masses. They are the second-lar ...
s, and debris from collisions), determining distances (actually
redshift
In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in fr ...
s) of galaxies or
quasar
A quasar is an extremely luminous active galactic nucleus (AGN). It is pronounced , and sometimes known as a quasi-stellar object, abbreviated QSO. This emission from a galaxy nucleus is powered by a supermassive black hole with a mass rangi ...
s, and identifying unfamiliar objects by analysis of their spectrum.
Balmer lines can appear as
absorption
Absorption may refer to:
Chemistry and biology
*Absorption (biology), digestion
**Absorption (small intestine)
*Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials
*Absorption (skin), a route by which s ...
or
emission lines in a spectrum, depending on the nature of the object observed. In
star
A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s, the Balmer lines are usually seen in absorption, and they are "strongest" in stars with a surface temperature of about 10,000
kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and ...
s (
spectral type
In astronomy, stellar classification is the classification of stars based on their spectral characteristics. Electromagnetic radiation from the star is analyzed by splitting it with a prism or diffraction grating into a spectrum exhibiting the ...
A). In the spectra of most spiral and irregular galaxies,
active galactic nuclei
An active galactic nucleus (AGN) is a compact region at the center of a galaxy that has a much-higher-than-normal luminosity over at least some portion of the electromagnetic spectrum with characteristics indicating that the luminosity is not prod ...
,
H II region
An H II region or HII region is a region of interstellar atomic hydrogen that is ionized. It is typically in a molecular cloud of partially ionized gas in which star formation has recently taken place, with a size ranging from one to hundreds ...
s and
planetary nebula
A nebula ('cloud' or 'fog' in Latin; pl. nebulae, nebulæ or nebulas) is a distinct luminescent part of interstellar medium, which can consist of ionized, neutral or molecular hydrogen and also cosmic dust. Nebulae are often star-forming regio ...
e, the Balmer lines are emission lines.
In stellar spectra, the H-epsilon line (transition 7→2, 397.007 nm) is often mixed in with another absorption line caused by ionized
calcium
Calcium is a chemical element with the symbol Ca and atomic number 20. As an alkaline earth metal, calcium is a reactive metal that forms a dark oxide-nitride layer when exposed to air. Its physical and chemical properties are most similar ...
known as "H" (the
original designation given by
Joseph von Fraunhofer
Joseph Ritter von Fraunhofer (; ; 6 March 1787 – 7 June 1826) was a German physicist and optical lens manufacturer. He made optical glass, an achromatic telescope, and objective lenses. He also invented the spectroscope and developed diffr ...
). H-epsilon is separated by 0.16 nm from Ca II H at 396.847 nm, and cannot be resolved in low-resolution spectra. The H-zeta line (transition 8→2) is similarly mixed in with a neutral
helium
Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic ta ...
line seen in hot stars.
See also
*
Astronomical spectroscopy
Astronomical spectroscopy is the study of astronomy using the techniques of spectroscopy to measure the spectrum of electromagnetic radiation, including visible light, ultraviolet, X-ray, infrared and radio waves that radiate from stars an ...
*
Bohr model
In atomic physics, the Bohr model or Rutherford–Bohr model, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar Syst ...
*
Hydrogen spectral series
The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are due to the electron making transitions between two energy levels in an ...
*
Lyman series In physics and chemistry, the Lyman series is a hydrogen spectral series of transitions and resulting ultraviolet emission lines of the hydrogen atom as an electron goes from ''n'' ≥ 2 to ''n'' = 1 (where ''n'' is the princip ...
*
Rydberg formula
In atomic physics, the Rydberg formula calculates the wavelengths of a spectral line in many chemical elements. The formula was primarily presented as a generalization of the Balmer series for all atomic electron transitions of hydrogen. It wa ...
*
Stellar classification
*
Notes
{{Hydrogen spectral series-footer
Emission spectroscopy
Hydrogen physics