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In
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
and
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...
, the Lyman series is a
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 i ...
of transitions and resulting
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 ...
emission line A spectral line is a weaker or stronger region in an otherwise uniform and continuous spectrum. It may result from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used ...
s of the
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 ...
atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...
as an
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 ...
goes from ''n'' ≥ 2 to ''n'' = 1 (where ''n'' is the
principal quantum number In quantum mechanics, the principal quantum number (''n'') of an electron in an atom indicates which electron shell or energy level it is in. Its values are natural numbers (1, 2, 3, ...). Hydrogen and Helium, at their lowest energies, have just ...
), the lowest energy level of the electron (groundstate). The transitions are named sequentially by
Greek letters The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC. It was derived from the earlier Phoenician alphabet, and is the earliest known alphabetic script to systematically write vowels as we ...
: from ''n'' = 2 to ''n'' = 1 is called Lyman-alpha, 3 to 1 is Lyman-beta, 4 to 1 is Lyman-gamma, and so on. The series is named after its discoverer, Theodore Lyman. The greater the difference in the principal quantum numbers, the higher the energy of the electromagnetic emission.


History

The first line in the spectrum of the Lyman series was discovered in 1906 by physicist Theodore Lyman IV, who was studying the ultraviolet spectrum of electrically excited hydrogen gas. The rest of the lines of the spectrum (all in the ultraviolet) were discovered by Lyman from 1906-1914. The spectrum of radiation emitted by hydrogen is non-continuous or discrete. Here is an illustration of the first series of hydrogen emission lines: Historically, explaining the nature of the hydrogen spectrum was a considerable problem in
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
. Nobody could predict the
wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
s of the hydrogen lines until 1885 when the Balmer formula gave an empirical formula for the visible hydrogen spectrum. Within five years Johannes Rydberg came up with an
empirical formula In chemistry, the empirical formula of a chemical compound is the simplest whole number ratio of atoms present in a compound. A simple example of this concept is that the empirical formula of sulfur monoxide, or SO, is simply SO, as is the empir ...
that solved the problem, presented first in 1888 and final form in 1890. Rydberg managed to find a formula to match the known
Balmer series The Balmer series, or Balmer lines in atomic physics, is one of a set of hydrogen spectral series, six named series describing the spectral line emissions of the hydrogen atom. The Balmer series is calculated using the Balmer formula, an empiri ...
emission lines, and also predicted those not yet discovered. Different versions of the Rydberg formula with different simple numbers were found to generate different series of lines. On December 1, 2011, it was announced that ''
Voyager 1 ''Voyager 1'' is a space probe launched by NASA on September 5, 1977, as part of the Voyager program to study the outer Solar System and the interstellar medium, interstellar space beyond the Sun's heliosphere. It was launched 16 days afte ...
'' detected the first Lyman-alpha radiation originating from the
Milky Way The Milky Way or Milky Way Galaxy is the galaxy that includes the Solar System, with the name describing the #Appearance, galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars in other arms of the galax ...
galaxy. Lyman-alpha radiation had previously been detected from other galaxies, but due to interference from the Sun, the radiation from the Milky Way was not detectable.


The Lyman series

The version 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 was ...
that generated the Lyman series was: = R_\text \left( 1 - \frac \right) \qquad \left( R_\text = R_\infty \frac \approx 1.096810^7\,\text^ \approx \frac \right) where ''n'' is a natural number greater than or equal to 2 (i.e., ). Therefore, the lines seen in the image above are the wavelengths corresponding to ''n'' = 2 on the right, to ''n'' →  on the left. There are infinitely many spectral lines, but they become very dense as they approach ''n'' →  (the Lyman limit), so only some of the first lines and the last one appear. The
wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
s in the Lyman series are all ultraviolet:


Explanation and derivation

In 1914, when
Niels Bohr Niels Henrik David Bohr (, ; ; 7 October 1885 – 18 November 1962) was a Danish theoretical physicist who made foundational contributions to understanding atomic structure and old quantum theory, quantum theory, for which he received the No ...
produced his
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 ...
theory, the reason why hydrogen spectral lines fit Rydberg's formula was explained. Bohr found that the electron bound to the hydrogen atom must have quantized energy levels described by the following formula, : E_n = - \frac\,\frac = - \frac. According to Bohr's third assumption, whenever an electron falls from an initial energy level ''E''i to a final energy level ''E''f, the atom must emit radiation with a wavelength of : \lambda = \frac. There is also a more comfortable notation when dealing with energy in units of
electronvolt In physics, an electronvolt (symbol eV), also written electron-volt and electron volt, is the measure of an amount of kinetic energy gained by a single electron accelerating through an Voltage, electric potential difference of one volt in vacuum ...
s and wavelengths in units of
angstrom The angstrom (; ) is a unit of length equal to m; that is, one ten-billionth of a metre, a hundred-millionth of a centimetre, 0.1 nanometre, or 100 picometres. The unit is named after the Swedish physicist Anders Jonas Ångström (1814–18 ...
s, : \lambda = \frac Å. Replacing the energy in the above formula with the expression for the energy in the hydrogen atom where the initial energy corresponds to energy level ''n'' and the final energy corresponds to energy level ''m'', : \frac = \frac = R_\text \left(\frac - \frac \right) Where ''R''H is the same
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 ...
for hydrogen from Rydberg's long known formula. This also means that the inverse of the Rydberg constant is equal to the Lyman limit. For the connection between Bohr, Rydberg, and Lyman, one must replace ''m'' with 1 to obtain : \frac = R_\text \left( 1 - \frac \right) which is Rydberg's formula for the Lyman series. Therefore, each wavelength of the emission lines corresponds to an electron dropping from a certain energy level (greater than 1) to the first energy level.


See also

*
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 ...
*
H-alpha Hydrogen-alpha, typically shortened to H-alpha or Hα, is a deep-red visible spectral line of the hydrogen atom with a wavelength of 656.28  nm in air and 656.46 nm in vacuum. It is the first spectral line in the Balmer series and is em ...
*
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 i ...
* K-alpha * Lyman-alpha line * Lyman continuum photon *
Moseley's law Moseley's law is an empirical law concerning the characteristic X-rays emitted by atoms. The law was discovered and published by the English physicist Henry Moseley in 1913–1914. Until Moseley's work, "atomic number" was merely an element's plac ...
*
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 was ...
*
Balmer series The Balmer series, or Balmer lines in atomic physics, is one of a set of hydrogen spectral series, six named series describing the spectral line emissions of the hydrogen atom. The Balmer series is calculated using the Balmer formula, an empiri ...


References

{{Hydrogen spectral series-footer Emission spectroscopy Hydrogen physics