Hydrogen atom - Citizendia

For other uses, see the physics of atomic hydrogen.

Hydrogen-1
Full table
General
Name, symbol	protium, ¹H
Neutrons	0
Protons	1
Nuclide Data
Natural abundance	99. Template talkIso1 -->The isotope table below shows Isotopes of the Chemical elements including all A table of Chemical elements ordered by Atomic number and color coded according to type of element A table of Chemical elements ordered by Atomic number and color coded according to type of element This article is a discussion of neutrons in general For the specific case of a neutron found outside the nucleus see Free neutron. The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive In Chemistry, natural abundance (NA refers to the abundance Isotopes of a Chemical element as naturally found on a planet 985%
Half-life	stable
Isotope mass	1. Half-Life (computer-game page here It's already listed in the disambiguation page The atomic mass (ma is the Mass of an atom most often expressed in unified atomic mass units The atomic mass may be considered to be the total mass 007825 u
Spin	½+
Excess energy	7288. The unified atomic mass unit ( u) or Dalton ( Da) or sometimes universal mass unit, is an unit of Mass used to express In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin Binding energy is the Mechanical energy required to disassemble a whole into separate parts 969 ± 0. 001 keV
Binding energy	0. Binding energy is the Mechanical energy required to disassemble a whole into separate parts 000 ± 0. 0000 keV

Depiction of a hydrogen atom showing the diameter as about twice the Bohr model radius. In Atomic physics, the Bohr model created by Niels Bohr depicts the Atom as a small positively charged nucleus surrounded by Electrons (Image not to scale)

A hydrogen atom is an atom of the chemical element hydrogen. Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 The electrically neutral atom contains a single positively-charged proton and a single negatively-charged electron bound to the nucleus by the Coulomb force. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form The most abundant isotope, hydrogen-1, protium, or light hydrogen, contains no neutrons; other isotopes contain one or more neutrons. Isotopes (Greek isos = "equal" tópos = "site place" are any of the different types of atoms ( Nuclides This article is a discussion of neutrons in general For the specific case of a neutron found outside the nucleus see Free neutron. This article primarily concerns hydrogen-1.

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. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons In Classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other

In 1913, Niels Bohr obtained the spectral frequencies of the hydrogen atom after making a number of simplifying assumptions. Niels Henrik David Bohr (nels ˈb̥oɐ̯ˀ in Danish 7 October 1885 – 18 November 1962 was a Danish Physicist who made fundamental contributions to understanding These assumptions, the cornerstones of the Bohr model, were not fully correct but did yield the correct energy answers. In Atomic physics, the Bohr model created by Niels Bohr depicts the Atom as a small positively charged nucleus surrounded by Electrons Bohr's results 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. In Physics, especially Quantum mechanics, the Schrödinger equation is an equation that describes how the Quantum state of a Physical system From this, the hydrogen energy levels and thus the frequencies of the hydrogen spectral lines can be calculated. A quantum mechanical system or particle that is bound, confined spacially can only take on certain discrete values of energy as opposed to classical particles which 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 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. Anisotropy (pronounced with stress on the third syllable ˌænaɪˈsɒtrəpi is the property of being directionally dependent as opposed to Isotropy, which means homogeneity

The Schrödinger equation also applies to more complicated atoms and molecules. In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by However, in most such cases the solution is not analytical and either computer calculations are necessary or simplifying assumptions must be made.

1 Solution of Schrödinger equation: Overview of results
2 Mathematical summary of eigenstates of hydrogen atom
3 Visualizing the hydrogen electron orbitals
4 Features going beyond the Schrödinger solution
- 4.1 Hydrogen Without its Electron
5 See also
6 References
7 External links

Solution of Schrödinger equation: Overview of results

The solution of the Schrödinger equation (wave equations) 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). ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form Isotropy is uniformity in all directions Precise definitions depend on the subject area 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. The Energy eigenstates of a quantum system are the set of Eigenvalues and Eigenvectors obtained by solving the time-independent Schrödinger equation Coordinates are numbers which describe the location of points in a plane or in space In Mathematics, given a Linear transformation, an of that linear transformation is a nonzero vector which when that transformation is applied to it changes In Quantum mechanics, the Hamiltonian H is the Observable corresponding to the Total energy of the system In Quantum mechanics, the angular momentum operator is an Operator analogous to classical Angular momentum. This corresponds to the fact that angular momentum is conserved in the orbital motion of the electron around the nucleus. The article on Magnetism states that the physical cause of an atomic magnetic dipole (or moment is two kinds of movement of electrons Therefore, the energy eigenstates may be classified by two angular momentum quantum numbers, l and m (integer numbers). Quantum numbers describe values of conserved numbers in the dynamics of the Quantum system. 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). In Mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834 &ndash 1886 are the Canonical solutions of Laguerre's equation 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). Generally speaking an object with rotational symmetry is an object that looks the same after a certain amount of Rotation. 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. In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin Therefore, any eigenstate of the electron in the hydrogen atom is described fully by four quantum numbers. In Mathematics, given a Linear transformation, an of that linear transformation is a nonzero vector which when that transformation is applied to it changes According to the usual rules of quantum mechanics, the actual state of the electron may be any superposition of these states. Quantum superposition is the fundamental law of Quantum mechanics. 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, quantization is a procedure for constructing a Quantum field theory starting from a classical field theory.

Mathematical summary of eigenstates of hydrogen atom

Main article: hydrogen-like atom

Energy levels

The energy levels of hydrogen, including fine structure are given by

$E_{nj} = \frac{-13.6 \ \mathrm{eV}}{n^2} \left(1 + \frac{\alpha^2}{n^2}\left(\frac{n}{j+\frac{1}{2}} - \frac{3}{4} \right) \right) \,$

where

α

is the fine-structure constant

j is an integer which is the angular momentum eigenvalue

The value of -13. A hydrogen-like atom is an Atom with one Electron and thus is Isoelectronic with Hydrogen. In Atomic physics, the fine structure describes the splitting of the Spectral lines of Atoms due to first order relativistic corrections The fine-structure constant or Sommerfeld fine-structure constant, usually denoted \alpha \ is the Fundamental physical constant characterizing 6 eV can be found from the simple Bohr model, and is related to the mass, m, and charge of the electron, q:

$-13.6 \ \mathrm{eV} = -\frac{m_e q_e^4}{8 h^2 \epsilon_{0}^2} .\,$

It is even more elegantly connected to fine-structure constant:

$-13.6 \ \mathrm{eV} = -\frac{m_e c^2 \,\alpha^2}{2} = -\frac{0.51\mathrm{MeV}}{2 \cdot 137^2} .$

Wavefunction

The normalized position wavefunctions, given in spherical coordinates are:

$\psi_{nlm}(r,\vartheta,\varphi) = \sqrt {{\left ( \frac{2}{n a_0} \right )}^3\frac{(n-l-1)!}{2n[(n+l)!]} } e^{- \rho / 2} \rho^{l} L_{n-l-1}^{2l+1}(\rho) \cdot Y_{lm}(\vartheta, \varphi )$

where:

$\rho = {2r \over {na_0}}$

a 0

is the Bohr radius. In Atomic physics, the Bohr model created by Niels Bohr depicts the Atom as a small positively charged nucleus surrounded by Electrons A wave function or wavefunction is a mathematical tool used in Quantum mechanics to describe any physical system In Mathematics, the spherical coordinate system is a Coordinate system for representing geometric figures in three dimensions using three coordinates the radial In the Bohr model of the structure of an Atom, put forward by Niels Bohr in 1913 Electrons orbit a central nucleus.

$L_{n-l-1}^{2l+1}(\rho)$ are the generalized Laguerre polynomials of degree n-l-1. In Mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834 &ndash 1886 are the Canonical solutions of Laguerre's equation

$Y_{lm}(\vartheta, \varphi ) \,$ is a spherical harmonic. In Mathematics, the spherical harmonics are the angular portion of an Orthogonal set of solutions to Laplace's equation represented in a system of

Angular momentum

The eigenvalues for Angular momentum operator:

$L^2 | n, l, m \rang = {\hbar}^2 l(l+1) | n, l, m \rang$

$L_z | n, l, m \rang = \hbar m | n, l, m \rang$

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). In Mathematics, given a Linear transformation, an of that linear transformation is a nonzero vector which when that transformation is applied to it changes In Quantum mechanics, the angular momentum operator is an Operator analogous to classical Angular momentum. These are cross-sections of the probability density that are color-coded (black=zero density, white=highest density). In Quantum mechanics, a probability amplitude is a complex -valued function that describes an uncertain or unknown quantity 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.

The "ground state", i. In Quantum mechanics, a stationary state is an Eigenstate of a Hamiltonian, or in other words a state of definite energy e. the state of lowest energy, in which the electron is usually found, is the first one, the "1s" state (principal quantum level n = 1, l = 0).

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 mass as predicted by special relativity. Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial Its mass and momentum increase by about one part in 37,000. Since the electron's wavelength is determined by its momentum, orbitals containing higher speed electrons show 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). Mercury (ˈmɜrkjʊri also called quicksilver or hydrargyrum, is a Chemical element with the symbol Hg ( Latinized hydrargyrum Gold (ˈɡoʊld is a Chemical element with the symbol Au (from its Latin name aurum) and Atomic number 79 Caesium or cesium (ˈsiːziəm is the Chemical element with the symbol Cs and Atomic number 55 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. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges In Physics, an inertial frame of reference is a Frame of reference which belongs to a set of frames in which Physical laws hold in the same and simplest The spin of the electron has an associated magnetic moment which interacts with this magnetic field. In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current This effect is also explained by special relativity, and it leads to the so-called spin-orbit coupling, i. In Quantum physics, the spin-orbit interaction (also called spin-orbit effect or spin-orbit coupling) is any interaction of a particle's spin e. , an interaction between the electron's orbital motion around the nucleus, and its spin. The article on Magnetism states that the physical cause of an atomic magnetic dipole (or moment is two kinds of movement of electrons In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin

Both of these features (and more) are incorporated in the relativistic Dirac equation, with predictions that come still closer to experiment. In Physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides 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). See also Azimuthal quantum number#Addition of quantized angular momenta In Quantum mechanics, the total angular quantum momentum numbers parameterize the total In Atomic physics, the spin quantum number is a Quantum number that parameterizes the intrinsic Angular momentum (or spin angular momentum or simply The Azimuthal quantum number (or orbital angular momentum quantum number, second quantum number) symbolized as l (lower-case L is a Quantum number States of the same j and the same n are still degenerate.

There are always vacuum fluctuations of the electromagnetic field, according to quantum mechanics. In Physics, a virtual particle is a particle that exists for a limited time and space introducing uncertainty in their energy and momentum due to the Heisenberg Uncertainty The electromagnetic field is a physical field produced by electrically charged objects. 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). In Physics, the Lamb shift, named after Willis Lamb (1913-2008 is a small difference in Energy between two Energy levels ^2S_{1/2} Quantum electrodynamics ( QED) is a relativistic Quantum field theory of Electrodynamics. Motivation and history When calculating Scattering cross sections in Particle physics, the interaction between particles can be described In Quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system This effect is now called Lamb shift. In Physics, the Lamb shift, named after Willis Lamb (1913-2008 is a small difference in Energy between two Energy levels ^2S_{1/2}

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.

Due to the high precision of the theory also very high precision for the experiments is needed, which utilize a frequency comb. A frequency comb is the graphic representation of the spectrum of a mode locked laser.

Hydrogen Without its Electron

There are numerous circumstances in which a Hydrogen atom may lose its electron, most of which involve bonding, such as HCL, or hydrochloric acid. Hydrochloric acid is the Solution of Hydrogen chloride ( H[[Chlorine Cl]] in water In such a case, the Hydrogen atom serves only as a proton. This is mostly true with the formation of acids, the amount of Hydrogen bonded will determine the strength of the acid. In Computer science, ACID ( Atomicity Consistency Isolation Durability) is a set of properties that guarantee that Database transactions are An example of a stronger acid would be H₂SO₄, known as Sulfuric Acid. Sulfuric (or sulphuric acid, H 2 S[[oxygen O]]4 is a strong Mineral acid. Three Hydrogen atoms are donated in H₃PO₄, or Phosphoric Acid. Phosphoric acid, also known as orthophosphoric acid or phosphoric(V acid, is a mineral (inorganic acid having the Chemical formula However, the overall pH of such compounds would be based on dilution. pH is the measure of the acidity or alkalinity of a Solution.

(no lighter isotopes)	Isotopes of Hydrogen	Hydrogen-2
Produced from: See proton emission	Decay chain	Decays to: Stable

References

Griffiths, David J. Deuterium, also called heavy hydrogen, is a Stable isotope of Hydrogen with a Natural abundance in the Oceans of Earth Tritium (ˈtɹɪtiəm symbol or, also known as Hydrogen-3) is a radioactive Isotope of Hydrogen. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons Quantum chemistry is a branch of Theoretical chemistry, which applies Quantum mechanics and Quantum field theory to address issues and problems in In quantum field theory (QFT the forces between particles are mediated by other particles In Quantum physics, a quantum state is a mathematical object that fully describes a quantum system. The theoretical and experimental justification for the Schrödinger equation motivates the discovery of the Schrödinger equation, the equation that describes the dynamics of Hydrogen ( H) (Standard atomic mass 100794(7 u) has three naturally occurring isotopes, denoted 1H 2H Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 Deuterium, also called heavy hydrogen, is a Stable isotope of Hydrogen with a Natural abundance in the Oceans of Earth Proton emission (also known as proton radioactivity is a type of radioactive decay in which a Proton is ejected from a nucleus. In Nuclear science, the decay chain refers to the Radioactive decay of different discrete radioactive decay products as a chained series of transformations David J Griffiths (born 1942 is a US physicist and educator He has worked at Reed College since 1978 where he is currently the Howard Vollum (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.

Bransden, B. H. ; C. J. Joachain (1983). Physics of Atoms and Molecules. London: Longman. ISBN 0-582-44401-2.

The Diameter of An Hydrogen atom is 12345355654767676mb

External links

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