
The
emission spectrum
The emission spectrum of a chemical element or chemical compound is the Spectrum (physical sciences), spectrum of frequencies of electromagnetic radiation emitted due to electrons making a atomic electron transition, transition from a high energ ...
of atomic
hydrogen
Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
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
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
making
transitions between two
energy level
A quantum mechanics, quantum mechanical system or particle that is bound state, bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical mechanics, classical pa ...
s in an atom. The classification of the series by the Rydberg formula was important in the development of
quantum mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
. The spectral series are important in
astronomical spectroscopy
Astronomical spectroscopy is the study of astronomy using the techniques of spectroscopy to measure the electromagnetic spectrum, spectrum of electromagnetic radiation, including Visible light astronomy, visible light, Ultraviolet astronomy, ultr ...
for detecting the presence of hydrogen and calculating
red shifts.
Physics

A hydrogen atom consists of an electron orbiting its
nucleus. The
electromagnetic force
In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interac ...
between the electron and the nuclear
proton
A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...
leads to a set of
quantum state
In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system ...
s for the electron, each with its own energy. These states were visualized by the
Bohr model
In atomic physics, the Bohr model or Rutherford–Bohr model was a model of the atom that incorporated some early quantum concepts. Developed from 1911 to 1918 by Niels Bohr and building on Ernest Rutherford's nuclear Rutherford model, model, i ...
of the hydrogen atom as being distinct orbits around the nucleus. Each energy level, or electron shell, or orbit, is designated by an integer, as shown in the figure. The Bohr model was later replaced by quantum mechanics in which the electron occupies an
atomic orbital
In quantum mechanics, an atomic orbital () is a Function (mathematics), function describing the location and Matter wave, wave-like behavior of an electron in an atom. This function describes an electron's Charge density, charge distribution a ...
rather than an orbit, but the allowed energy levels of the hydrogen atom remained the same as in the earlier theory.
Spectral emission occurs when an electron transitions, or jumps, from a higher energy state to a lower energy state. To distinguish the two states, the lower energy state is commonly designated as , and the higher energy state is designated as . The energy of an emitted
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 particles that can ...
corresponds to the energy difference between the two states. Because the energy of each state is fixed, the energy difference between them is fixed, and the transition will always produce a photon with the same energy.
The spectral lines are grouped into series according to . Lines are named sequentially starting from the longest wavelength/lowest frequency of the series, using Greek letters within each series. For example, the line is called "Lyman-alpha" (Ly-α), while the line is called "Paschen-delta" (Pa-δ).

There are emission lines from hydrogen that fall outside of these series, such as the
21 cm line. These emission lines correspond to much rarer atomic events such as
hyperfine transitions.
The
fine structure also results in single spectral lines appearing as two or more closely grouped thinner lines, due to relativistic corrections.
In quantum mechanical theory, the discrete spectrum of atomic emission was based on the
Schrödinger equation
The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after E ...
, which is mainly devoted to the study of energy spectra of
hydrogen-like atoms, whereas the time-dependent
equivalent Heisenberg equation is convenient when studying an atom driven by an external
electromagnetic wave
In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength, ...
.
In the processes of absorption or emission of photons by an atom, the
conservation laws hold for the whole
isolated system
In physical science, an isolated system is either of the following:
# a physical system so far removed from other systems that it does not interact with them.
# a thermodynamic system enclosed by rigid immovable walls through which neither ...
, such as an atom plus a photon. Therefore the motion of the electron in the process of photon absorption or emission is always accompanied by motion of the nucleus, and, because the mass of the nucleus is always finite, the energy spectra of hydrogen-like atoms must
depend on the nuclear mass.
Rydberg formula
The energy differences between levels in the Bohr model, and hence the wavelengths of emitted or absorbed photons, is given by the Rydberg formula:
where
The wavelength will always be positive because is defined as the lower level and so is less than . This equation is valid for all hydrogen-like species, i.e. atoms having only a single electron, and the particular case of hydrogen spectral lines is given by ''Z'' = 1.
Series
Lyman series ( = 1)

In the Bohr model, the Lyman series includes the lines emitted by transitions of the electron from an outer orbit of quantum number n > 1 to the 1st orbit of quantum number n' = 1.
The series is named after its discoverer,
Theodore Lyman, who discovered the spectral lines from 1906–1914. All the wavelengths in the Lyman series are in the
ultraviolet
Ultraviolet radiation, also known as simply UV, is electromagnetic radiation of wavelengths of 10–400 nanometers, shorter than that of visible light, but longer than X-rays. UV radiation is present in sunlight and constitutes about 10% of ...
band.
Balmer series ( = 2)

The Balmer series includes the lines due to transitions from an outer orbit n > 2 to the orbit n' = 2.
Named after
Johann Balmer, who discovered the Balmer formula, an
empirical
Empirical evidence is evidence obtained through sense experience or experimental procedure. It is of central importance to the sciences and plays a role in various other fields, like epistemology and law.
There is no general agreement on how t ...
equation to predict the Balmer series, in 1885. Balmer lines are historically referred to as "
H-alpha", "H-beta", "H-gamma" and so on, where H is the element hydrogen. Four of the Balmer lines are in the technically "visible" part of the spectrum, with wavelengths longer than 400 nm and shorter than 700 nm. Parts of the Balmer series can be seen in the
solar spectrum. H-alpha is an important line used in astronomy to detect the presence of hydrogen.
Paschen series (Bohr series, = 3)
Named after the
German physicist
Friedrich Paschen who first observed them in 1908. The Paschen lines all lie in the
infrared
Infrared (IR; sometimes called infrared light) is electromagnetic radiation (EMR) with wavelengths longer than that of visible light but shorter than microwaves. The infrared spectral band begins with the waves that are just longer than those ...
band. This series overlaps with the next (Brackett) series, i.e. the shortest line in the Brackett series has a wavelength that falls among the Paschen series. All subsequent series overlap.
Brackett series ( = 4)
Named after the American physicist
Frederick Sumner Brackett who first observed the spectral lines in 1922. The spectral lines of Brackett series lie in far infrared band.
Pfund series ( = 5)
Experimentally discovered in 1924 by
August Herman Pfund.
Humphreys series ( = 6)
Discovered in 1953 by American physicist
Curtis J. Humphreys.
Further series ( > 6)
Further series are unnamed, but follow the same pattern and equation as dictated by the Rydberg equation. Series are increasingly spread out and occur at increasing wavelengths. The lines are also increasingly faint, corresponding to increasingly rare atomic events. The seventh series of atomic hydrogen was first demonstrated experimentally at infrared wavelengths in 1972 by Peter Hansen and John Strong at the University of Massachusetts Amherst.
Extension to other systems
The concepts of the Rydberg formula can be applied to any system with a single particle orbiting a nucleus, for example a
He+ ion or a
muonium exotic atom. The equation must be modified based on the system's
Bohr radius; emissions will be of a similar character but at a different range of energies. The
Pickering–Fowler series was originally attributed to an unknown form of hydrogen with half-integer transition levels by both
Pickering and
Fowler, but Bohr correctly recognised them as spectral lines arising from the He
+ ion.
All other atoms have at least two electrons in their
neutral form and the interactions between these electrons makes analysis of the spectrum by such simple methods as described here impractical. The deduction of the Rydberg formula was a major step in physics, but it was long before an extension to the spectra of other elements could be accomplished.
See also
*
Astronomical spectroscopy
Astronomical spectroscopy is the study of astronomy using the techniques of spectroscopy to measure the electromagnetic spectrum, spectrum of electromagnetic radiation, including Visible light astronomy, visible light, Ultraviolet astronomy, ultr ...
* The
hydrogen line (21 cm)
*
Lamb shift
In physics, the Lamb shift, named after Willis Lamb, is an anomalous difference in energy between two electron orbitals in a hydrogen atom. The difference was not predicted by theory and it cannot be derived from the Dirac equation, which pre ...
*
Moseley's law
*
Quantum optics
Quantum optics is a branch of atomic, molecular, and optical physics and quantum chemistry that studies the behavior of photons (individual quanta of light). It includes the study of the particle-like properties of photons and their interaction ...
References
External links
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Hydrogen physics
Emission spectroscopy
Hydrogen