Depiction of a hydrogen atom showing the diameter as about twice the Bohr model radius. (Image not to scale) A hydrogen atom is an atom of the chemical element hydrogen. It is composed of a single negatively-charged electron circling a single positively-charged nucleus of the hydrogen atom. The nucleus of hydrogen consists of only a single proton (in the case of hydrogen-1 or protium; see box at right), or it may also include one or more neutrons (giving deuterium, tritium, and other isotopes). The electron is bound to the nucleus by the Coulomb force. Image File history File links Download high resolution version (730x685, 12 KB) hydrogen-1 isotope Created by user:oo64eva using Macromedia Fireworks 4. ...
This isotope table shows all of the known isotopes of the chemical elements, arranged with increasing atomic numbers (proton numbers) from left to right and increasing neutron numbers from top to bottom. ...
An isotope is a form of an element with a different number of neutrons. ...
This article or section does not adequately cite its references or sources. ...
In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ...
Natural abundance refers to the prevalence of different isotopes of an element as found in nature. ...
Half-Life For a quantity subject to exponential decay, the half-life is the time required for the quantity to fall to half of its initial value. ...
The atomic mass (ma) is the mass of an atom at rest, most often expressed in unified atomic mass units. ...
The atomic mass unit (amu), unified atomic mass unit (u), or dalton (Da), is a small unit of mass used to express atomic masses and molecular masses. ...
In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ...
Binding energy is the energy required to disassemble a whole into separate parts. ...
Kev can refer to either: A regional term for the chav social group in the United Kingdom An abbreviation - keV - of the unit Kiloelectronvolt An abbreviation for the given name Kevin. ...
Binding energy is the energy required to disassemble a whole into separate parts. ...
Image File history File links Hydrogen_atom. ...
Image File history File links Hydrogen_atom. ...
The Bohr model of the hydrogen atom, where negatively charged electrons confined to atomic shells encircle a small positively charged atomic nucleus, and that an electron jump between orbits must be accompanied by an emitted or absorbed amount of electromagnetic energy hν. The orbits that the electrons travel in are...
General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ...
e- redirects here. ...
The nucleus of an atom is the very small dense region, of positive charge, in its centre consisting of nucleons (protons and neutrons). ...
Deuterium, also called heavy hydrogen, is a stable isotope of hydrogen with a natural abundance in the oceans of Earth of approximately one atom in 6500 of hydrogen (~154 PPM). ...
Tritium (symbol T or 3H) is a radioactive isotope of hydrogen. ...
In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrical force that one stationary, electrically charged substance of small volume (ideally, a point source) exerts on another. ...
The hydrogen atom has special significance in quantum mechanics and quantum field theory as a simple two-body problem physical system which has yielded many simple analytical solutions in closed-form. Fig. ...
In classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other. ...
In mathematics, an equation or system of equations is said to have a closed-form solution if, and only if, at least one solution can be expressed analytically in terms of a bounded number of well-known operations. ...
In 1913, Niels Bohr obtained the spectral frequencies of the hydrogen atom after making a number of simplifying assumptions. These assumptions were not fully correct, but did yield the correct energy answers (see The Bohr Model). The results of Bohr for the frequencies and underlying energy values were confirmed by the full quantum-mechanical analysis which uses the Schrödinger equation, as was shown in 1925/26. The solution to the Schrödinger equation for hydrogen is analytical. From this solution, the hydrogen energy levels and thus the frequencies of the hydrogen spectral lines) can be calculated. The solution of the Schrödinger equation goes much further than the Bohr model however, because it also yields the shape of the electron's wave function ("orbital") for the various possible quantum-mechanical states-- thus explaining the anisotropic character of atomic bonds. Niels (Henrik David) Bohr (October 7, 1885 – November 18, 1962) was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in 1922. ...
The Bohr model of the atom The Bohr Model is a physical model that depicts the atom as a small positively charged nucleus with electrons in orbit at different levels, similar in structure to the solar system. ...
In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the space- and time-dependence of quantum mechanical systems. ...
In mathematics, an equation or system of equations is said to have a closed-form solution if, and only if, at least one solution can be expressed analytically in terms of a bounded number of well-known operations. ...
An energy level is a quantified stable energy, which a physical system can have; the term is most commonly used in reference to the electron configuration of electrons, in atoms or molecules. ...
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from an excess or deficiency of photons in a narrow frequency range, compared with the nearby frequencies. ...
This article is being considered for deletion in accordance with Wikipedias deletion policy. ...
The Schrödinger equation also applies to more complicated atoms and molecules, however, in most such cases the solution is not analytical and either computer calculations are necessary, or else simplifying assumptions must be made. In science, a molecule is a group of atoms in a definite arrangement held together by chemical bonds. ...
Solution of Schrödinger equation: Overview of results
The solution of the Schrödinger equation for the hydrogen atom uses the fact that the Coulomb potential produced by the nucleus is isotropic (it is radially symmetric in space and only depends on the distance to the nucleus). Although the resulting energy eigenfunctions (the "orbitals") are not necessarily isotropic themselves, their dependence on the angular coordinates follows completely generally from this isotropy of the underlying potential: The eigenstates of the Hamiltonian (= energy eigenstates) can be chosen as simultaneous eigenstates of the angular momentum operator. This corresponds to the fact that angular momentum is conserved in the orbital motion of the electron around the nucleus. Therefore, the energy eigenstates may be classified by two angular momentum quantum numbers, l and m (integer numbers). The "angular momentum" quantum number l = 0, 1, 2, ... determines the magnitude of the angular momentum. The "magnetic" quantum number m = −l, .., +l determines the projection of the angular momentum on the (arbitrarily chosen) z-axis. Coulombs torsion balance In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ...
Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ...
The Energy eigenstates of a quantum system are the set of eigenvalues and eigenvectors obtained by solving the time-independent Schroedinger equation for the system in question, where is the time-independent Hamiltonian operator, is the nth energy eigenvector (also known as eigenfunction or wavefunction), and is the nth energy...
This article describes some of the common coordinate systems that appear in elementary mathematics. ...
In quantum mechanics, operators correspond to observable variables, eigenvectors are also called eigenstates, and the eigenvalues of an operator represent those values of the corresponding variable that have non-zero probability of occurring. ...
The quantum Hamiltonian is the physical state of a system, which may be characterized as a ray in an abstract Hilbert space (or, in the case of ensembles, as a trace class operator with trace 1). ...
In quantum mechanics, angular momentum is defined like momentum - not as a quantity but as an operator on the wave function: where r and p are the position and momentum operators respectively. ...
In the article on Magnetism, it states that the physical cause of an atomic magnetic dipole (or moment) is two kinds of movement of electrons. ...
A quantum number describes the energies of electrons in atoms. ...
In addition to mathematical expressions for total angular momentum and angular momentum projection of wavefunctions, an expression for the radial dependence of the wave functions must be found. It is only here that the details of the 1/r Coulomb potential enter (leading to Laguerre polynomials in r). This leads to a third quantum number, the principal quantum number n = 1, 2, 3, ... The principal quantum number in hydrogen is related to atom's total energy. In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834 - 1886), are a polynomial sequence defined by These polynomials are orthogonal to each other with respect to the inner product given by Also, for each n, Ln(x) is a solution of Laguerres equation which is a second-order...
Note that the maximum value of the angular momentum quantum number is limited by the principal quantum number: it can run only up to n − 1, i.e. l = 0, 1, ..., n − 1.
Due to angular momentum conservation, states of the same l but different m have the same energy (this holds for all problems with rotational symmetry). In addition, for the hydrogen atom, states of the same n but different l are also degenerate (i.e. they have the same energy). However, this is a specific property of hydrogen and is no longer true for more complicated atoms which have a (effective) potential differing from the form 1/r (due to the presence of the inner electrons shielding the nucleus potential). The triskelion appearing on the Isle of Man flag. ...
The word degeneracy has more than one meaning: In general, degeneracy means reverting to an earlier, simpler, state In mathematics, a limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. ...
Taking into account the spin of the electron adds a last quantum number, the projection of the electron's spin angular momentum along the z axis, which can take on two values. Therefore, any eigenstate of the electron in the hydrogen atom is described fully by four quantum numbers. According to the usual rules of quantum mechanics, the actual state of the electron may be any superposition of these states. This explains also why the choice of z-axis for the directional quantization of the angular momentum vector is immaterial: An orbital of given l and m' obtained for another preferred axis z' can always be represented as a suitable superposition of the various states of different m (but same l) that have been obtained for z. In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ...
In linear algebra, the eigenvectors (from the German eigen meaning inherent, characteristic) of a linear operator are non-zero vectors which, when operated on by the operator, result in a scalar multiple of themselves. ...
Quantum superposition is the application of the superposition principle to quantum mechanics. ...
In physics, quantization is a procedure for constructing a quantum field theory starting from a classical field theory. ...
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Mathematical summary of eigenstates of hydrogen atom -
Main article: hydrogen-like atom Hydrogen-like atoms are atoms with one single electron. ...
Energy levels The energy levels of hydrogen, including fine structure are given by 1. ...
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 - where
- α is the fine-structure constant
- j is an integer which is the angular momentum eigenvalue
The value of 13.6 eV can be found from the simple Bohr model, and is related to the mass, m, and charge of the electron, q: The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ...
The Bohr model of the hydrogen atom, where negatively charged electrons confined to atomic shells encircle a small positively charged atomic nucleus, and that an electron jump between orbits must be accompanied by an emitted or absorbed amount of electromagnetic energy hν. The orbits that the electrons travel in are...
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Wavefunction The normalized position wavefunctions, given in spherical coordinates are: This article discusses the concept of a wavefunction as it relates to quantum mechanics. ...
This article describes some of the common coordinate systems that appear in elementary mathematics. ...
![psi_{nlm}(r,theta,phi) = sqrt {{left ( frac{2}{n a_0} right )}^3frac{(n-l-1)!}{2n[(n+l)!]} } e^{- rho / 2} rho^{l} L_{n-l-1}^{2l+1}(rho) cdot Y_{l,m}(theta, phi )](http://upload.wikimedia.org/math/f/a/3/fa36c367c22322c56f530b49d6c58b69.png) where:  - a0 is the Bohr radius.
 are the Generalized Laguerre polynomials of degree n-l-1. is a spherical harmonic. In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central nucleus. ...
In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834 - 1886), are a polynomial sequence defined by These polynomials are orthogonal to each other with respect to the inner product given by Also, for each n, Ln(x) is a solution of Laguerres equation which is a second-order...
Spherical Harmonic is a fantasy novel by Catherine Asaro which tells the story of Pharaoh Dyhianna (Dehya) Selei, ruler of the Skolian Imperialate, after the Radiance War fought by the Imperialate and their enemy Eubian Concord. ...
Angular momentum The eigenvalues for Angular momentum operator: In mathematics, a number is called an eigenvalue of a matrix if there exists a nonzero vector such that the matrix times the vector is equal to the same vector multiplied by the eigenvalue. ...
In quantum mechanics, angular momentum is defined like momentum - not as a quantity but as an operator on the wave function: where r and p are the position and momentum operators respectively. ...
 
Visualizing the hydrogen electron orbitals
 Probability densities for the electron at different quantum numbers (l) The image to the right shows the first few hydrogen atom orbitals (energy eigenfunctions). These are cross-sections of the probability density that are color-coded (black=zero density, white=highest density). The angular momentum quantum number l is denoted in each column, using the usual spectroscopic letter code ("s" means l = 0; "p": l = 1; "d": l = 2). The main quantum number n (= 1, 2, 3, ...) is marked to the right of each row. For all pictures the magnetic quantum number m has been set to 0, and the cross-sectional plane is the xz-plane (z is the vertical axis). The probability density in three-dimensional space is obtained by rotating the one shown here around the z-axis. Image File history File links HAtomOrbitals. ...
In quantum mechanics, a probability amplitude is a complex-valued function that describes an uncertain or unknown quantity. ...
The "ground state", i.e. the state of lowest energy, in which the electron is usually found, is the first one, the "1s" state (n = 1, l = 0). In physics, the ground state of a quantum mechanical system is its lowest-energy state. ...
An image with more orbitals is also available (up to higher numbers n and l).
Note the number of black lines that occur in each but the first orbital. These are "nodal lines" (which are actually nodal surfaces in three dimensions). Their total number is always equal to n − 1, which is the sum of the number of radial nodes (equal to n - l - 1) and the number of angular nodes (equal to l).
Features going beyond the Schrödinger solution There are several important effects that are neglected by the Schrödinger equation and which are responsible for certain small but measurable deviations of the real spectral lines from the predicted ones: - Although the mean speed of the electron in hydrogen is only 1/137th of the speed of light there is an increase in the electron's momentum which is not quite linear with velocity, as predicted by special relativity. The relativistic mass of the electron may be said to increase. Since the electron's wavelength is determined by its momentum, orbitals containing electrons reaching higher speeds show differential contraction due to smaller wavelengths. For elements with high atomic number Z, this effect is more pronounced, and especially so for s electrons, which move at relativistic velocities as they penetrate the screening electrons near the core of high Z atoms. This relativistic mass effect for electrons causes a contraction of 6s orbitals relative to 5d orbitals (by comparison to corresponding s and d electrons in lighter elements in the same column of the periodic table); this results in 6s valence electrons becoming lowered in energy. Examples of significant physical outcomes of this effect include the lowered melting temperature of mercury (which results from 6s electrons not being available for metal bonding) and the golden color of gold and caesium (which result from narrowing of 6s to 5d transition energy to the point that visible light begins to be absorbed). See [1] and [2]).
- Even when there is no external magnetic field, in the inertial frame of the moving electron, the electromagnetic field of the nucleus has a magnetic component. The spin of the electron has an associated magnetic moment which interacts with this magnetic field. This effect is also explained by special relativity, and it leads to the so-called spin-orbit coupling, i.e., an interaction between the electron's orbital motion around the nucleus, and its spin.
Both of these features (and more) are incorporated in the relativistic Dirac equation, with predictions that come still closer to experiment. Again the Dirac equation may be solved analytically in the special case of a two-body system, such as the hydrogen atom. The resulting solution quantum states now must be classified by the total angular momentum number j (arising through the coupling between electron spin and orbital angular momentum). States of the same j and the same n are still degenerate. A line showing the speed of light on a scale model of Earth and the Moon The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. It is the speed of all electromagnetic radiation...
The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest...
The term mass in special relativity can be used in different ways, occasionally leading to confusion. ...
General Name, Symbol, Number mercury, Hg, 80 Chemical series transition metals Group, Period, Block 12, 6, d Appearance silvery Standard atomic weight 200. ...
GOLD refers to one of the following: GOLD (IEEE) is an IEEE program designed to garner more student members at the university level (Graduates of the Last Decade). ...
General Name, Symbol, Number caesium, Cs, 55 Chemical series alkali metals Group, Period, Block 1, 6, s Appearance silvery gold Atomic mass 132. ...
In physics, a magnetic field is a force field that surrounds electric current circuits. ...
In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ...
A bar magnet. ...
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In the article on Magnetism, it states that the physical cause of an atomic magnetic dipole (or moment) is two kinds of movement of electrons. ...
In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ...
In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ...
The total angular quantum momentum numbers parameterize the total angular momentum of a given electron, by combining its orbital angular momentum and its intrinsic angular momentum (i. ...
In atomic physics, the spin quantum number is a quantum number that parametrizes the intrinsic angular momentum (or spin angular momentum, or simply spin) of a given particle. ...
The Azimuthal quantum number (or orbital angular momentum quantum number) l is a quantum number for an atomic orbital which determines its orbital angular momentum. ...
For these developments, it was essential that the solution of the Dirac equation for the hydrogen atom could be worked out exactly, such that any experimentally observed deviation had to be taken seriously as a signal of failure of the theory. In the description of the interaction between elementary particles in quantum field theory, a virtual particle is a temporary elementary particle, used to describe an intermediate stage in the interaction. ...
The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ...
In physics, the Lamb shift, named after Willis Lamb, is a small difference in energy between two energy levels and of the hydrogen atom in quantum mechanics. ...
Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ...
In this Feynman diagram, an electron and positron annihilate and become a quark-antiquark pair. ...
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. ...
In physics, the Lamb shift, named after Willis Lamb, is a small difference in energy between two energy levels and of the hydrogen atom in quantum mechanics. ...
Due to the high precision of the theory also very high precision for the experiments is needed, which utilize a frequency comb. An ultrashort pulse of light in the time domain. ...
See also General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ...
Fig. ...
Quantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. ...
Quantum field theory (QFT) is the quantum theory of fields. ...
A quantum state is any possible state in which a quantum mechanical system can be. ...
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. ...
Isotopes are any of the several different forms of an element each having different atomic mass (mass number). ...
General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ...
Deuterium (symbol 2H) is a stable isotope of hydrogen with a natural abundance of one atom in 6500 of hydrogen. ...
Proton emission (also known as proton radioactivity) is a type of radioactive decay in which a proton is ejected from a nucleus. ...
Nearly all the decay products of radioactive decay are themselves radioactive. ...
References - Griffiths, David J. (1995). Introduction to Quantum Mechanics. Upper Saddle River, NJ: Prentice Hall. ISBN 0-13-111892-7.
Section 4.2 deals with the hydrogen atom specifically, but all of Chapter 4 is relevant. David J. Griffiths is a U.S. physicist and educator. ...
- Bransden, B.H.; C.J. Joachain (1983). Physics of Atoms and Molecules. London: Longman. ISBN 0-582-44401-2.
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