Information about Hydrogen Atom
This article is about the physics of atomic hydrogen. For the chemistry of diatomic hydrogen, see hydrogen.
- Atomic hydrogen redirects here. For the method of welding, see Atomic hydrogen welding.
Hydrogen-1 
General Name, symbol protium, 1H Neutrons 0 Protons 1 Nuclide Data Natural abundance 99.985% Half-life stable Isotope mass 1.007825 u Spin ½+ Excess energy 7288.969 0.001 keV Binding energy 0.000 0.0000 keV
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. This article is primarily about Hydrogen-1, also known as protium or "light hydrogen", which is the primary component of natural hydrogen.
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.
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.
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.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.
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.
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).
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.Mathematical summary of eigenstates of hydrogen atom
Energy levels
The energy levels of hydrogen, including fine structure are given by- :
- where
- :
is the fine-structure constant
- :j is an integer which is the angular momentum eigenvalue
- :
- :
Wavefunction
The normalized position wavefunctions, given in spherical coordinates are:
is the Bohr radius.
are the generalized Laguerre polynomials of degree n-l-1.
is a spherical harmonic.
Angular momentum
The eigenvalues for Angular momentum operator:Visualizing the hydrogen electron orbitals
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.
Probability densities for the electron at different quantum numbers (l)
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).
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 http://www.chem1.com/acad/webtut/atomic/qprimer/#Q26 and http://www.bama.ua.edu/~chem/seminars/student_seminars/spring04/papers-s04/gutowski-sem.pdf#search=%22relativistic%20effects%20gold%20mercury%22).
- 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.
- There are always vacuum fluctuations of the electromagnetic field, according to quantum mechanics. Due to such fluctuations degeneracy between states of the same j but different l is lifted, giving them slightly different energies. This has been demonstrated in the famous Lamb-Retherford experiment and was the starting point for the development of the theory of Quantum electrodynamics (which is able to deal with these vacuum fluctuations and employs the famous Feynman diagrams for approximations using perturbation theory). This effect is now called Lamb shift.
Due to the high precision of the theory also very high precision for the experiments is needed, which utilize a frequency comb.See also
- Hydrogen
- quantum mechanics
- quantum chemistry
- quantum field theory
- quantum state
- Theoretical and experimental justification for the Schrödinger equation
(no lighter isotopes) Isotopes of Hydrogen Hydrogen-2 Produced from:
See proton emissionDecay chain Decays to:
StableReferences
- Griffiths-1995">Griffiths, David J. (1995). Introduction to Quantum Mechanics. Upper Saddle River, NJ: Prentice Hall. ISBN 0-13-111892-7.
- Bransden, B.H.; C.J. Joachain (1983). Physics of Atoms and Molecules. London: Longman. ISBN 0-582-44401-2.
External links
- Physics of hydrogen atom on Scienceworld
- Interactive graphical representation of orbitals
- Applet which allows viewing of all sorts of hydrogenic orbitals
- The Hydrogen Atom: Wave Functions, and Probability Density "pictures"
- Basic Quantum Mechanics of the Hydrogen Atom
1, −1
(amphoteric oxide)
Electronegativity 2.20 (Pauling scale) More
Atomic radius 25 pm
Atomic radius (calc.) 53 pm
Covalent radius 37 pm
Van der Waals radius 120 pm
Miscellaneous
Thermal conductivity (300 K) 180.
..... Click the link for more information.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.
..... Click the link for more information.Atomic hydrogen welding (AHW) is an arc welding process that uses an arc between two metal tungsten electrodes in a shielding atmosphere of hydrogen. The process was invented by Irving Langmuir in the course of his studies in atomic hydrogen.
..... Click the link for more information.This isotope table shows about 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.
..... Click the link for more information.An isotope a type of neutral atom but the number of neutrons is different from the number of protons in the nucleus. May be radioactive.Elements 1-15
Hydrogen
..... Click the link for more information.An isotope a type of neutral atom but the number of neutrons is different from the number of protons in the nucleus. May be radioactive.Elements 1-15
Hydrogen
..... Click the link for more information.Neutron
The quark structure of the neutron.
Composition: one up, two down
Family: Fermion
Group: Quark
Interaction: Gravity, Electromagnetic, Weak, Strong
Antiparticle: Antineutron
Discovered: James Chadwick[1]
Symbol: n
Mass: 1.
..... Click the link for more information.Proton
The quark structure of the proton.
Composition: 2 up, 1 down
Family: Fermion
Group: Quark
Interaction: Gravity, Electromagnetic, Weak, Strong
Antiparticle: Antiproton
Discovered: Ernest Rutherford (1919)
Symbol: p+
Mass: 1.
..... Click the link for more information.In chemistry, natural abundance (NA) refers to the prevalence of isotopes of a chemical element as naturally found on a planet. The relative atomic mass (a weighted average) of these isotopes is the atomic weight listed for the element in the periodic table.
..... Click the link for more information.- For , see .
..... Click the link for more information.atomic mass (ma) is the mass of an atom at rest, most often expressed in unified atomic mass units.[1] The atomic mass may be considered to be the total mass of protons, neutrons and electrons in a single atom (when the atom is motionless).
..... Click the link for more information.The unified atomic mass unit (u), or dalton (Da), is a small unit of mass used to express atomic and molecular masses. It is defined to be one twelfth of the mass of an unbound atom of the carbon-12 nuclide, at rest and in its ground state.
..... Click the link for more information.spin is 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 classical mechanics, the spin angular momentum
..... Click the link for more information.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.
- The fictional character Kev Hawkins.
- A word used to describe a Boy racer.
..... Click the link for more information.Binding energy is the mechanical energy required to disassemble a whole into separate parts. A bound system has a lower potential energy than its constituent parts; this is what keeps the system together.
..... Click the link for more information.1, −1
(amphoteric oxide)
Electronegativity 2.20 (Pauling scale) More
Atomic radius 25 pm
Atomic radius (calc.) 53 pm
Covalent radius 37 pm
Van der Waals radius 120 pm
Miscellaneous
Thermal conductivity (300 K) 180.
..... Click the link for more information.Electron
Theoretical estimates of the electron density for the first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density
Composition: Elementary particle
Family: Fermion
Group: Lepton
Generation: First
..... Click the link for more information.The nucleus of an atom is the very small dense region of an atom, in its center consisting of nucleons (protons and neutrons). The size (diameter) of the nucleus is in the range of 1.
..... Click the link for more information.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). Deuterium thus accounts for approximately 0.015% (on a weight basis, 0.
..... Click the link for more information.Tritium (symbol T or ³H) is a radioactive isotope of hydrogen. The nucleus of tritium (sometimes called triton) contains one proton and two neutrons, whereas the nucleus of protium (the most abundant hydrogen isotope) contains no neutrons. Its atomic mass is 3.
..... Click the link for more information.Coulomb's law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated as follows:- The magnitude of the electrostatic force between two points electric charges is directly proportional to the product of the magnitudes of each
..... Click the link for more information.quantum mechanics is the study of the relationship between energy quanta (radiation) and matter, in particular that between valence shell electrons and photons. Quantum mechanics is a fundamental branch of physics with wide applications in both experimental and theoretical physics.
..... Click the link for more information.two-body problem is to determine the motion of two point particles that interact only with each other. Common examples include a satellite orbiting a planet, a planet orbiting a star, two stars orbiting each other (a binary star), and a classical electron orbiting an atomic nucleus.
..... Click the link for more information.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 certain "well-known" functions.
..... Click the link for more information.Niels Bohr
Niels Henrik David Bohr
Born September 7 1885
Copenhagen, Denmark
Died November 18 1962 (aged 77)
..... Click the link for more information.In atomic physics, the Bohr model 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, rather than
..... Click the link for more information.Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1926, describes the space- and time-dependence of quantum mechanical systems. It is of central importance in non-relativistic quantum mechanics, playing a role for microscopic particles analogous to
..... Click the link for more information.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 certain "well-known" functions.
..... Click the link for more information.energy levels are possible. The term energy level is most commonly used in reference to the electron configuration in atoms or molecules. In other words, the energy spectrum can be quantized (see continuous spectrum for the more general case).
..... Click the link for more information.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.
..... Click the link for more information.
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