Balmer series

Balmer series

Overview
The Balmer series or Balmer lines in atomic physics
Atomic physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and...

, is the designation of one of a set of six different named series describing the spectral line
Spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...

 emissions of the hydrogen atom
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...

.
The Balmer series is calculated using the Balmer formula, an empirical
Empirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....

 equation discovered by Johann Balmer in 1885.

The visible spectrum
Spectrum
A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...

 of light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

 from hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

 displays four wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

s, 410 nm, 434 nm, 486 nm, and 656 nm, that correspond to emissions of photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s by electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s in excited states transitioning to the quantum level described by the principal quantum number
Principal quantum number
In atomic physics, the principal quantum symbolized as n is the firstof a set of quantum numbers of an atomic orbital. The principal quantum number can only have positive integer values...

 n equals 2.
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Encyclopedia
The Balmer series or Balmer lines in atomic physics
Atomic physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and...

, is the designation of one of a set of six different named series describing the spectral line
Spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...

 emissions of the hydrogen atom
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...

.
The Balmer series is calculated using the Balmer formula, an empirical
Empirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....

 equation discovered by Johann Balmer in 1885.

The visible spectrum
Spectrum
A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...

 of light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

 from hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

 displays four wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

s, 410 nm, 434 nm, 486 nm, and 656 nm, that correspond to emissions of photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s by electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s in excited states transitioning to the quantum level described by the principal quantum number
Principal quantum number
In atomic physics, the principal quantum symbolized as n is the firstof a set of quantum numbers of an atomic orbital. The principal quantum number can only have positive integer values...

 n equals 2. There are also a number of ultraviolet
Ultraviolet
Ultraviolet light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than X-rays, in the range 10 nm to 400 nm, and energies from 3 eV to 124 eV...

 Balmer lines with wavelengths shorter than 400 nm.

Overview


The Balmer series is characterized by the electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

 transitioning from n ≥ 3 to n = 2, where n refers to the radial quantum number or principal quantum number
Principal quantum number
In atomic physics, the principal quantum symbolized as n is the firstof a set of quantum numbers of an atomic orbital. The principal quantum number can only have positive integer values...

 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
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....

, these lines are historically referred to as "H-alpha", "H-beta", "H-gamma" and so on, where H is the element hydrogen.
Transition of 3→2 4→2 5→2 6→2 7→2 8→2 9→2 →2
Name H-α H-β H-γ H-δ H-ε H-ζ H-η
Wavelength (nm) 656.3 486.1 434.1 410.2 397.0 388.9 383.5 364.6
Color Red
Red
Red is any of a number of similar colors evoked by light consisting predominantly of the longest wavelengths of light discernible by the human eye, in the wavelength range of roughly 630–740 nm. Longer wavelengths than this are called infrared , and cannot be seen by the naked eye...

Cyan
Cyan
Cyan from , transliterated: kýanos, meaning "dark blue substance") may be used as the name of any of a number of colors in the blue/green range of the spectrum. In reference to the visible spectrum cyan is used to refer to the color obtained by mixing equal amounts of green and blue light or the...

Blue
Blue
Blue is a colour, the perception of which is evoked by light having a spectrum dominated by energy with a wavelength of roughly 440–490 nm. It is considered one of the additive primary colours. On the HSV Colour Wheel, the complement of blue is yellow; that is, a colour corresponding to an equal...

Violet
Violet (color)
As the name of a color, violet is synonymous with a bluish purple, when the word "purple" is used in the common English language sense of any color between blue and red, not including either blue or red...

(Ultraviolet
Ultraviolet
Ultraviolet light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than X-rays, in the range 10 nm to 400 nm, and energies from 3 eV to 124 eV...

)
(Ultraviolet) (Ultraviolet) (Ultraviolet)


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 absorption/emission lines of hydrogen with high accuracy. Balmer's equation inspired the Rydberg equation as a generalization of it, and this in turn led physicists to find the Lyman
Lyman series
In physics and chemistry, the Lyman series is the series of transitions and resulting ultraviolet emission lines of the hydrogen atom as an electron goes from n ≥ 2 to n = 1...

, Paschen, and Brackett series which predicted other absorption/emission lines of hydrogen found outside the visible spectrum
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 wavelengths from about 390 to 750 nm. In terms of...

.

The familiar red H-alpha
H-alpha
H-alpha is a specific red visible spectral line created by hydrogen with a wavelength of 656.28 nm, which occurs when a hydrogen electron falls from its third to second lowest energy level...

 spectral line of hydrogen gas, which is the transition from the shell n = 3 to the Balmer series shell n = 2, is one of the conspicuous colors of the universe. It contributes a bright red line to the spectra of emission
Emission nebula
An emission nebula is a cloud of ionized gas emitting light of various colors. The most common source of ionization is high-energy photons emitted from a nearby hot star...

 or ionization nebula, like the Orion Nebula
Orion Nebula
The Orion Nebula is a diffuse nebula situated south of Orion's Belt. It is one of the brightest nebulae, and is visible to the naked eye in the night sky. M42 is located at a distance of and is the closest region of massive star formation to Earth. The M42 nebula is estimated to be 24 light...

, which are often H II region
H II region
An H II region is a large, low-density cloud of partially ionized gas in which star formation has recently taken place. The short-lived, blue stars forged in these regions emit copious amounts of ultraviolet light, ionizing the surrounding gas...

s found in star forming regions. In true-color pictures, these nebula have a distinctly pink color from the combination of visible Balmer lines that hydrogen emits.

Later, it was discovered that when the spectral lines of the hydrogen spectrum are examined at very high resolution, they are found to be closely spaced doublets. This splitting is called fine structure
Fine structure
In atomic physics, the fine structure describes the splitting of the spectral lines of atoms due to first order relativistic corrections.The gross structure of line spectra is the line spectra predicted by non-relativistic electrons with no spin. For a hydrogenic atom, the gross structure energy...

. It was also found that excited electrons could jump to the Balmer series n=2 from orbitals where n was greater than 6, emitting shades of violet when doing so.

Balmer's formula


Balmer noticed that a single number had a relation to every line in the hydrogen spectrum that was in the visible light region. That number was 364.56 nm. When any integer higher than 2 was squared and then divided by itself squared minus 4, then that number multiplied by 364.56 (see equation below) gave a wavelength of another line in the hydrogen spectrum. By this formula, he was able to show that certain measurements of lines made in his time by spectroscopy
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...

 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
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

 of the absorption/emission lines and was originally presented as follows (save for a notation change to give Balmer's constant as B):


Where is the wavelength.
B is a constant with the value of 3.6456×10-7 m or 364.56 nm.
n is equal to 2
m is an integer such that m > n.


In 1888 the physicist Johannes Rydberg
Johannes Rydberg
Johannes Robert Rydberg, , , was a Swedish physicist mainly known for devising the Rydberg formula, in 1888, which is used to predict the wavelengths of photons emitted by changes in the energy level of an electron in a hydrogen atom.The physical constant known as the...

 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
Rydberg formula
The Rydberg formula is used in atomic physics to describe the wavelengths of spectral lines of many chemical elements. It was formulated by the Swedish physicist Johannes Rydberg, and presented on November 5, 1888.-History:...

 and follows as a simple reciprocal mathematical rearrangement of the formula above (conventionally using a notation of n for m as the single integral constant needed):


where λ is the wavelength of the absorbed/emitted light and RH is the Rydberg constant
Rydberg constant
The Rydberg constant, symbol R∞, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to atomic spectra in the science of spectroscopy. Rydberg initially determined its value empirically from spectroscopy, but Niels Bohr later showed that its value could be calculated...

 for hydrogen. The Rydberg constant is seen to be equal to in Balmer's formula, and this value, for an infinitely heavy nucleus, is meter) = 10,973,731.57 meter−1.

Role in astronomy


The Balmer series is particularly useful in astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

 because the Balmer lines appear in numerous stellar objects due to the abundance of hydrogen in the universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

, and therefore are commonly seen and relatively strong compared to lines from other elements.

The spectral classification
Stellar classification
In astronomy, stellar classification is a classification of stars based on their spectral characteristics. The spectral class of a star is a designated class of a star describing the ionization of its chromosphere, what atomic excitations are most prominent in the light, giving an objective measure...

 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 are very important. Other characteristics of a star can be determined by close analysis of its spectrum include surface gravity
Surface gravity
The surface gravity, g, of an astronomical or other object is the gravitational acceleration experienced at its surface. The surface gravity may be thought of as the acceleration due to gravity experienced by a hypothetical test particle which is very close to the object's surface and which, in...

 (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
Radial velocity
Radial velocity is the velocity of an object in the direction of the line of sight . In astronomy, radial velocity most commonly refers to the spectroscopic radial velocity...

 due to doppler shifting of the Balmer lines. This has important uses all over astronomy, from detecting binary star
Binary star
A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, comes, or secondary...

s, exoplanets, compact objects such as neutron star
Neutron star
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

s and black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

s (by the motion of hydrogen in accretion disks around them), identifying groups of objects with similar motions and presumably origins (moving groups, star cluster
Star cluster
Star clusters or star clouds are groups of stars. Two types of star clusters can be distinguished: globular clusters are tight groups of hundreds of thousands of very old stars which are gravitationally bound, while open clusters, more loosely clustered groups of stars, generally contain less than...

s, galaxy cluster
Galaxy cluster
A galaxy cluster is a compact cluster of galaxies. Basic difference between a galaxy group and a galaxy cluster is that there are many more galaxies in a cluster than in a group. Also, galaxies in a cluster are more compact and have higher velocity dispersion. One of the key features of cluster is...

s, and debris from collisions), determining distances (actually redshift
Redshift
In physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...

s) of galaxies or quasar
Quasar
A quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...

s, 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 star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s, the Balmer lines are usually seen in absorption, and they are "strongest" in stars with a surface temperature of about 10,000 kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

 (spectral type A). In the spectra of most spiral and irregular galaxies, AGNs, H II region
H II region
An H II region is a large, low-density cloud of partially ionized gas in which star formation has recently taken place. The short-lived, blue stars forged in these regions emit copious amounts of ultraviolet light, ionizing the surrounding gas...

s and planetary
Planetary nebula
A planetary nebula is an emission nebula consisting of an expanding glowing shell of ionized gas ejected during the asymptotic giant branch phase of certain types of stars late in their life...

 nebula
Nebula
A nebula is an interstellar cloud of dust, hydrogen gas, helium gas and other ionized gases...

e, the Balmer lines are emission lines.

In stellar spectra, the H-epsilon line (transition 7-2) is often mixed in with another absorption line caused by ionized calcium
Calcium
Calcium is the chemical element with the symbol Ca and atomic number 20. It has an atomic mass of 40.078 amu. Calcium is a soft gray alkaline earth metal, and is the fifth-most-abundant element by mass in the Earth's crust...

 known by astronomers as "H" (the original designation
Fraunhofer lines
In physics and optics, the Fraunhofer lines are a set of spectral lines named for the German physicist Joseph von Fraunhofer . The lines were originally observed as dark features in the optical spectrum of the Sun....

 given by Fraunhofer
Joseph von Fraunhofer
Joseph von Fraunhofer was a German optician. He is known for the discovery of the dark absorption lines known as Fraunhofer lines in the Sun's spectrum, and for making excellent optical glass and achromatic telescope objectives.-Biography:Fraunhofer was born in Straubing, Bavaria...

). That is, 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 8-2) is similarly mixed in with a neutral helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...

 line seen in hot stars.

See also

  • Hydrogen spectral series
    Hydrogen spectral series
    The emission spectrum of atomic hydrogen is divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are due to electrons moving between energy levels in the atom. The spectral series are important in astronomy for detecting the presence...

  • Astronomical spectroscopy
    Astronomical spectroscopy
    Astronomical spectroscopy is the technique of spectroscopy used in astronomy. The object of study is the spectrum of electromagnetic radiation, including visible light, which radiates from stars and other celestial objects...

  • Stellar classification
    Stellar classification
    In astronomy, stellar classification is a classification of stars based on their spectral characteristics. The spectral class of a star is a designated class of a star describing the ionization of its chromosphere, what atomic excitations are most prominent in the light, giving an objective measure...

  • Bohr model
    Bohr model
    In atomic physics, the Bohr model, introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with electrostatic forces providing attraction,...

  • Theoretical and experimental justification for the Schrödinger equation
    Theoretical and experimental justification for the Schrödinger equation
    The theoretical and experimental justification for the Schrödinger equation motivates the discovery of the Schrödinger equation, the equation that describes the dynamics of nonrelativistic particles...

  • Rydberg formula
    Rydberg formula
    The Rydberg formula is used in atomic physics to describe the wavelengths of spectral lines of many chemical elements. It was formulated by the Swedish physicist Johannes Rydberg, and presented on November 5, 1888.-History:...