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 atom. The classification of the series by the Rydberg formula was important in the development of quantum mechanics. The spectral series are important in astronomical spectroscopy for detecting the presence of hydrogen and calculating red shifts.
A hydrogen atom consists of an electron orbiting its nucleus. The electromagnetic force between the electron and the nuclear proton leads to a set of quantum states for the electron, each with its own energy. These states were visualized by the Bohr model of the hydrogen atom as being distinct orbits around the nucleus. Each energy level, or electron shell, or orbit, is designated by an integer, n as shown in the figure. The Bohr model was later replaced by quantum mechanics in which the electron occupies an atomic orbital 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 n′, and the higher energy state is designated as n. The energy of an emitted photon 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 n′. Lines are named sequentially starting from the longest wavelength/lowest frequency of the series, using Greek letters within each series. For example, the 2 → 1 line is called "Lyman-alpha" (Ly-α), while the 7 → 3 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. [1] The fine structure also results in single spectral lines appearing as two or more closely grouped thinner lines, due to relativistic corrections. [2]
In quantum mechanical theory, the discrete spectrum of atomic emission was based on the Schrödinger equation, 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. [3]
In the processes of absorption or emission of photons by an atom, the conservation laws hold for the whole isolated system, 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. [3]
The energy differences between levels in the Bohr model, and hence the wavelengths of emitted or absorbed photons, is given by the Rydberg formula: [4]
where
The wavelength will always be positive because n′ is defined as the lower level and so is less than n. 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.
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 band. [7] [8]
| n | λ, vacuum (nm) |
|---|---|
| 2 | 121.57 |
| 3 | 102.57 |
| 4 | 97.254 |
| 5 | 94.974 |
| 6 | 93.780 |
| ∞ | 91.175 |
| Source: [9] | |
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 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. [10] 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.
| n | λ, air (nm) |
|---|---|
| 3 | 656.3  |
| 4 | 486.1  |
| 5 | 434.0  |
| 6 | 410.2  |
| 7 | 397.0  |
| ∞ | 364.6 |
| Source: [9] | |
Named after the German physicist Friedrich Paschen who first observed them in 1908. The Paschen lines all lie in the infrared band. [11] 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.
| n | λ, air (nm) |
|---|---|
| 4 | 1875 |
| 5 | 1282 |
| 6 | 1094 |
| 7 | 1005 |
| 8 | 954.6 |
| ∞ | 820.4 |
| Source: [9] | |
Named after the American physicist Frederick Sumner Brackett who first observed the spectral lines in 1922. [12] The spectral lines of Brackett series lie in far infrared band.
| n | λ, air (nm) |
|---|---|
| 5 | 4051 |
| 6 | 2625 |
| 7 | 2166 |
| 8 | 1944 |
| 9 | 1817 |
| ∞ | 1458 |
| Source: [9] | |
Experimentally discovered in 1924 by August Herman Pfund. [13]
| n | λ, vacuum (nm) |
|---|---|
| 6 | 7460 |
| 7 | 4654 |
| 8 | 3741 |
| 9 | 3297 |
| 10 | 3039 |
| ∞ | 2279 |
| Source: [14] | |
Discovered in 1953 by American physicist Curtis J. Humphreys. [15]
| n | λ, vacuum (μm) |
|---|---|
| 7 | 12.37 |
| 8 | 7.503 |
| 9 | 5.908 |
| 10 | 5.129 |
| 11 | 4.673 |
| ∞ | 3.282 |
| Source: [14] | |
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. [16]
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 [17] [18] [19] and Fowler, [20] but Bohr correctly recognised them as spectral lines arising from the He+ ion. [21] [22] [23]
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.
In atomic physics, the Bohr model or Rutherford–Bohr model was the first successful model of the atom. Developed from 1911 to 1918 by Niels Bohr and building on Ernest Rutherford's nuclear model, it supplanted the plum pudding model of J J Thomson only to be replaced by the quantum atomic model in the 1920s. It consists of a small, dense nucleus surrounded by orbiting electrons. It is analogous to the structure of the Solar System, but with attraction provided by electrostatic force rather than gravity, and with the electron energies quantized.
Spectroscopy is the field of study that measures and interprets electromagnetic spectra. In narrower contexts, spectroscopy is the precise study of color as generalized from visible light to all bands of the electromagnetic spectrum.
A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of the electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules. The energy spectrum of a system with such discrete energy levels is said to be quantized.
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 to identify atoms and molecules. These "fingerprints" can be compared to the previously collected ones of atoms and molecules, and are thus used to identify the atomic and molecular components of stars and planets, which would otherwise be impossible.
In spectroscopy, the Rydberg constant, symbol for heavy atoms or for hydrogen, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to the electromagnetic spectra of an atom. The constant first arose as an empirical fitting parameter in the Rydberg formula for the hydrogen spectral series, but Niels Bohr later showed that its value could be calculated from more fundamental constants according to his model of the atom.
Johannes (Janne) Robert Rydberg was a Swedish physicist mainly known for devising the Rydberg formula, in 1888, which is used to describe the wavelengths of photons emitted by changes in the energy level of an electron in a hydrogen atom.
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 first empirically stated in 1888 by the Swedish physicist Johannes Rydberg, then theoretically by Niels Bohr in 1913, who used a primitive form of quantum mechanics. The formula directly generalizes the equations used to calculate the wavelengths of the hydrogen spectral series.
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to electrons making a transition from a high energy state to a lower energy state. The photon energy of the emitted photons is equal to the energy difference between the two states. There are many possible electron transitions for each atom, and each transition has a specific energy difference. This collection of different transitions, leading to different radiated wavelengths, make up an emission spectrum. Each element's emission spectrum is unique. Therefore, spectroscopy can be used to identify elements in matter of unknown composition. Similarly, the emission spectra of molecules can be used in chemical analysis of substances.
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 emitted when an electron falls from a hydrogen atom's third- to second-lowest energy level. H-alpha has applications in astronomy where its emission can be observed from emission nebulae and from features in the Sun's atmosphere, including solar prominences and the chromosphere.
The Balmer series, or Balmer lines in atomic physics, is one of a set of six named series describing the spectral line emissions of the hydrogen atom. The Balmer series is calculated using the Balmer formula, an empirical equation discovered by Johann Balmer in 1885.
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, the lowest energy level of the electron (groundstate). The transitions are named sequentially by Greek letters: 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.
In quantum mechanics, an excited state of a system is any quantum state of the system that has a higher energy than the ground state. Excitation refers to an increase in energy level above a chosen starting point, usually the ground state, but sometimes an already excited state. The temperature of a group of particles is indicative of the level of excitation.
Johann Jakob Balmer was a Swiss mathematician best known for his work in physics, the Balmer series of hydrogen atom.
A Rydberg atom is an excited atom with one or more electrons that have a very high principal quantum number, n. The higher the value of n, the farther the electron is from the nucleus, on average. Rydberg atoms have a number of peculiar properties including an exaggerated response to electric and magnetic fields, long decay periods and electron wavefunctions that approximate, under some conditions, classical orbits of electrons about the nuclei. The core electrons shield the outer electron from the electric field of the nucleus such that, from a distance, the electric potential looks identical to that experienced by the electron in a hydrogen atom.
The Rydberg–Ritz combination principle is an empirical rule proposed by Walther Ritz in 1908 to describe the relationship of the spectral lines for all atoms, as a generalization of an earlier rule by Johannes Rydberg for the hydrogen atom and the alkali metals. The principle states that the spectral lines of any element include frequencies that are either the sum or the difference of the frequencies of two other lines. Lines of the spectra of elements could be predicted from existing lines. Since the frequency of light is proportional to the wavenumber or reciprocal wavelength, the principle can also be expressed in terms of wavenumbers which are the sum or difference of wavenumbers of two other lines.
Lyman continuum photons, shortened to Ly continuum photons or Lyc photons, are the photons emitted from stars or active galactic nuclei at photon energies above the Lyman limit. Hydrogen is ionized by absorbing LyC. Working from Victor Schumann's discovery of ultraviolet light, from 1906 to 1914, Theodore Lyman observed that atomic hydrogen absorbs light only at specific frequencies and the Lyman series is thus named after him. All the wavelengths in the Lyman series are in the ultraviolet band. This quantized absorption behavior occurs only up to an energy limit, known as the ionization energy. In the case of neutral atomic hydrogen, the minimum ionization energy is equal to the Lyman limit, where the photon has enough energy to completely ionize the atom, resulting in a free proton and a free electron. Above this energy, all wavelengths of light may be absorbed. This forms a continuum in the energy spectrum; the spectrum is continuous rather than composed of many discrete lines, which are seen at lower energies.
The history of quantum mechanics is a fundamental part of the history of modern physics. The major chapters of this history begin with the emergence of quantum ideas to explain individual phenomena—blackbody radiation, the photoelectric effect, solar emission spectra—an era called the Old or Older quantum theories. Building on the technology developed in classical mechanics, the invention of wave mechanics by Erwin Schrödinger and expansion by many others triggers the "modern" era beginning around 1925. Paul Dirac's relativistic quantum theory work lead him to explore quantum theories of radiation, culminating in quantum electrodynamics, the first quantum field theory. The history of quantum mechanics continues in the history of quantum field theory. The history of quantum chemistry, theoretical basis of chemical structure, reactivity, and bonding, interlaces with the events discussed in this article.
The Pickering series (also known as the Pickering–Fowler series) consists of three lines of singly ionised helium found, usually in absorption, in the spectra of hot stars like Wolf–Rayet stars. The name comes from Edward Charles Pickering and Alfred Fowler. The lines are produced by transitions from a higher energy level of an electron to a level with principal quantum number n = 4. The lines have wavelengths:
Modern spectroscopy in the Western world started in the 17th century. New designs in optics, specifically prisms, enabled systematic observations of the solar spectrum. Isaac Newton first applied the word spectrum to describe the rainbow of colors that combine to form white light. During the early 1800s, Joseph von Fraunhofer conducted experiments with dispersive spectrometers that enabled spectroscopy to become a more precise and quantitative scientific technique. Since then, spectroscopy has played and continues to play a significant role in chemistry, physics and astronomy. Fraunhofer observed and measured dark lines in the Sun's spectrum, which now bear his name although several of them were observed earlier by Wollaston.
The diffuse series is a series of spectral lines in the atomic emission spectrum caused when electrons jump between the lowest p orbital and d orbitals of an atom. The total orbital angular momentum changes between 1 and 2. The spectral lines include some in the visible light, and may extend into ultraviolet or near infrared. The lines get closer and closer together as the frequency increases never exceeding the series limit. The diffuse series was important in the development of the understanding of electron shells and subshells in atoms. The diffuse series has given the letter d to the d atomic orbital or subshell.
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