atomic orbital - wikipedia, the free encyclopedia

Electron atomic and molecular orbitals. The chart of orbitals(left) is arranged by increasing energy (see Madelung rule).Note that atomic orbits are functions of three variables

(two angles, and the distance from the nucleus, r).These images are faithful to the angular component of

the orbital, but not entirely representative of the orbitalas a whole.

Atomic orbitalFrom Wikipedia, the free encyclopedia

An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pairof electrons in an atom.[1] This function can be used to calculate the probability of finding any electron of an atom inany specific region around the atom's nucleus. These functions may serve as three-dimensional graph of anelectron’s likely location. The term may thus refer directly to the physical region defined by the function where theelectron is likely to be.[2] Specifically, atomic orbitals are the possible quantum states of an individual electron in thecollection of electrons around a single atom, as described by the orbital function.

Despite the obvious analogy to planets revolving around the Sun, electrons cannot be described as solid particlesand so atomic orbitals rarely, if ever, resemble a planet's elliptical path. A more accurate analogy might be that of alarge and often oddly-shaped atmosphere (the electron), distributed around a relatively tiny planet (the atomicnucleus). Atomic orbitals exactly describe the shape of this atmosphere only when a single electron is present in anatom. When more electrons are added to a single atom, the additional electrons tend to more evenly fill in a volumeof space around the nucleus so that the resulting collection (sometimes termed the atom’s “electron cloud” [3]) tendstoward a generally spherical zone of probability describing where the atom’s electrons will be found.

The idea that electrons might revolve around acompact nucleus with definite angular momentumwas convincingly argued in 1913 by Niels Bohr,[4]

and the Japanese physicist Hantaro Nagaokapublished an orbit-based hypothesis for electronicbehavior as early as 1904.[5] However, it was notuntil 1926 that the solution of the Schrödingerequation for electron-waves in atoms provided thefunctions for the modern orbitals.[6]

Because of the difference from classical mechanicalorbits, the term "orbit" for electrons in atoms, hasbeen replaced with the term orbital—a term firstcoined by chemist Robert Mulliken in 1932.[7]

Atomic orbitals are typically described as“hydrogen-like” (meaning one-electron) wavefunctions over space, categorized by n, l, and mquantum numbers, which correspond to theelectrons' energy, angular momentum, and anangular momentum direction, respectively. Eachorbital is defined by a different set of quantumnumbers and contains a maximum of two electrons.The simple names s orbital, p orbital, d orbitaland f orbital refer to orbitals with angularmomentum quantum number l = 0, 1, 2 and 3respectively. These names indicate the orbital shapeand are used to describe the electron configurationsas shown on the right. They are derived from thecharacteristics of their spectroscopic lines: sharp,principal, diffuse, and fundamental, the rest beingnamed in alphabetical order (omitting j).[8][9]

From about 1920, even before the advent ofmodern quantum mechanics, the aufbau principle(construction principle) that atoms were built up ofpairs of electrons, arranged in simple repeatingpatterns of increasing odd numbers (1,3,5,7..), hadbeen used by Niels Bohr and others to infer thepresence of something like atomic orbitals within the

8/12/2010 Atomic orbital - Wikipedia, the free enc…

en.wikipedia.org/wiki/Atomic_orbital 1/9

Computed hydrogen atom orbital for n=6, l=0, m=0total electron configuration of complex atoms. In themathematics of atomic physics, it is also oftenconvenient to reduce the electron functions ofcomplex systems into combinations of the simpler atomic orbitals. Although each electron in a multi-electron atom isnot confined to one of the “one-or-two-electron atomic orbitals” in the idealized picture above, still the electronwave-function may be broken down into combinations which still bear the imprint of atomic orbitals; as though, insome sense, the electron cloud of a many-electron atom is still partly “composed” of atomic orbitals, eachcontaining only one or two electrons. The physicality of this view is best illustrated in the repetitive nature of thechemical and physical behavior of elements which results in the natural ordering known from the 19th century as theperiodic table of the elements. In this ordering, the repeating periodicity of 2, 6, 10, and 14 elements in the periodictable corresponds with the total number of electrons which occupy a complete set of s, p, d and f atomic orbitals,respectively.

Contents1 Orbital names2 Formal quantum mechanical definition3 Connection to uncertainty relation4 Hydrogen-like atoms5 Qualitative characterization

5.1 Limitations on the quantum numbers

6 The shapes of orbitals6.1 Orbitals table

7 Orbital energy8 Electron placement and the periodic table

8.1 Relativistic effects

9 See also10 References11 Further reading12 External links

Orbital namesOrbitals are given names in the form:

where X is the energy level corresponding to the principal quantum number n, type is a lower-case letter denotingthe shape or subshell of the orbital and it corresponds to the angular quantum number l, and y is the number ofelectrons in that orbital.

For example, the orbital 1s2 (pronounced "one ess two") has two electrons and is the lowest energy level (n = 1)and has an angular quantum number of l = 0. In X-ray notation, the principal quantum number is given a letterassociated with it. For n = 1, 2, 3, 4, 5, ..., the letters associated with those numbers are K, L, M, N, O, ...respectively.

Formal quantum mechanical definitionIn quantum mechanics, the state of an atom, i.e. the eigenstates of the atomic Hamiltonian, is expanded (seeconfiguration interaction expansion and basis (linear algebra)) into linear combinations of anti-symmetrized products(Slater determinants) of one-electron functions. The spatial components of these one-electron functions are calledatomic orbitals. (When one considers also their spin component, one speaks of atomic spin orbitals.)

In atomic physics, the atomic spectral lines correspond to transitions (quantum leaps) between quantum states of anatom. These states are labelled by a set of quantum numbers summarized in the term symbol and usually associated



to particular electron configurations, i.e. by occupations schemes of atomic orbitals (e.g. 1s2 2s2 2p6 for theground state of neon -- term symbol: 1S0).

This notation means that the corresponding Slater determinants have a clear higher weight in the configurationinteraction expansion. The atomic orbital concept is therefore a key concept for visualizing the excitation processassociated to a given transition. For example, one can say for a given transition that it corresponds to the excitationof an electron from an occupied orbital to a given unoccupied orbital. Nevertheless one has to keep in mind thatelectrons are fermions ruled by Pauli exclusion principle and cannot be distinguished from the other electrons in theatom. Moreover, it sometimes happens that the configuration interaction expansion converges very slowly and thatone cannot speak about simple one-determinantal wave function at all. This is the case when electron correlation islarge.

Fundamentally, an atomic orbital is a one-electron wavefunction, even though most electrons do not exist in one-electron atoms, and so the one-electron view is an approximation. When thinking about orbitals, we are often givenan orbital vision which (even if it is not spelled out) is heavily influenced by this Hartree–Fock approximation, whichis one way to reduce the complexities of molecular orbital theory.

Connection to uncertainty relationImmediately after Heisenberg formulated his uncertainty relation, it was noted by Bohr that the existence of any sortof wave packet implies uncertainty in the wave frequency and wavelength, since a spread of frequencies is neededto create the packet itself. In quantum mechanics, where all particle momenta are associated with waves, it is theformation of such a wave packet which localizes the wave, and thus the particle, in space. In states where aquantum mechanical particle is bound, it must be localized as a wave packet, and the existence of the packet and itsminimum size implies a spread and minimal value in particle wavelength, and thus also momentum and energy. Inquantum mechanics, as a particle is localized to a smaller region in space, the associated compressed wave packetrequires a larger and larger range of momenta, and thus larger kinetic energy. Thus, the binding energy to contain ortrap a particle in a smaller region of space, increases without bound, as the region of space grows smaller. Particlescannot be restricted to a geometric point in space, since this would require an infinite particle momentum.

In chemistry, Schrödinger, Pauling, Mulliken and others noted that the consequence of Heisenberg's relation wasthat the electron, as a wave packet, could not be considered to have an exact location in its orbital. Max Bornsuggested that the electron's position needed to be described by a probability distribution which was connectedwith finding the electron at some point in the wave-function which described its associated wave packet. The newquantum mechanics did not give exact results, but only the probabilities for the occurrence of a variety of possiblesuch results. Heisenberg held that the path of a moving particle has no meaning if we cannot observe it, as wecannot with electrons in an atom.

In the quantum picture of Heisenberg, Schrödinger and others, the Bohr atom number n for each orbital becameknown as an n-sphere in a three dimensional atom and was pictured as the mean energy of the probability cloud ofthe electron's wave packet which surrounded the atom.

Although Heisenberg used infinite sets of positions for the electron in his matrices, this does not mean that theelectron could be anywhere in the universe.[citation needed] Rather there are several laws that show the electronmust be in one localized probability distribution. An electron is described by its energy in Bohr's atom which wascarried over to matrix mechanics. Therefore, an electron in a certain n-sphere had to be within a certain range fromthe nucleus depending upon its energy.[citation needed] This restricts its location.

Hydrogen-like atomsMain article: Hydrogen-like atom

The simplest atomic orbitals are those that occur in an atom with a single electron, such as the hydrogen atom. Inthis case the atomic orbitals are the eigenstates of the hydrogen Hamiltonian. They can be obtained analytically (seehydrogen atom). An atom of any other element ionized down to a single electron is very similar to hydrogen, and theorbitals take the same form.

For atoms with two or more electrons, the governing equations can only be solved with the use of methods ofiterative approximation. Orbitals of multi-electron atoms are qualitatively similar to those of hydrogen, and in thesimplest models, they are taken to have the same form. For more rigorous and precise analysis, the numerical



approximations must be used.

A given (hydrogen-like) atomic orbital is identified by unique values of three quantum numbers: n, l, and ml. Therules restricting the values of the quantum numbers, and their energies (see below), explain the electron configurationof the atoms and the periodic table.

The stationary states (quantum states) of the hydrogen-like atoms are its atomic orbital. However, in general, anelectron's behavior is not fully described by a single orbital. Electron states are best represented by time-depending"mixtures" (linear combinations) of multiple orbitals. See Linear combination of atomic orbitals molecular orbitalmethod.

The quantum number n first appeared in the Bohr model. It determines, among other things, the distance of theelectron from the nucleus; all electrons with the same value of n lie at the same distance. Modern quantummechanics confirms that these orbitals are closely related. For this reason, orbitals with the same value of n are saidto comprise a "shell". Orbitals with the same value of n and also the same value of l are even more closely related,and are said to comprise a "subshell".

Qualitative characterization

Limitations on the quantum numbers

An atomic orbital is uniquely identified by the values of the three quantum numbers, and each set of the threequantum numbers corresponds to exactly one orbital, but the quantum numbers only occur in certain combinationsof values. The rules governing the possible values of the quantum numbers are as follows:

The principal quantum number n is always a positive integer. In fact, it can be any positive integer, but for reasonsdiscussed below, large numbers are seldom encountered. Each atom has, in general, many orbitals associated witheach value of n; these orbitals together are sometimes called electron shells.

The azimuthal quantum number is a non-negative integer. Within a shell where n is some integer n0, rangesacross all (integer) values satisfying the relation . For instance, the n = 1 shell has only orbitalswith , and the n = 2 shell has only orbitals with , and . The set of orbitals associated with aparticular value of are sometimes collectively called a subshell.

The magnetic quantum number is also always an integer. Within a subshell where is some integer , ranges thus: .

The above results may be summarized in the following table. Each cell represents a subshell, and lists the values of available in that subshell. Empty cells represent subshells that do not exist.

l = 0 1 2 3 4 ...

n = 1 ml = 02 0 -1, 0, 1

3 0 -1, 0, 1 -2, -1, 0, 1, 2

4 0 -1, 0, 1 -2, -1, 0, 1, 2 -3, -2, -1, 0, 1, 2, 3

5 0 -1, 0, 1 -2, -1, 0, 1, 2 -3, -2, -1, 0, 1, 2, 3 -4, -3, -2 -1, 0, 1, 2, 3, 4

... ... ... ... ... ... ...

Subshells are usually identified by their n- and -values. n is represented by its numerical value, but isrepresented by a letter as follows: 0 is represented by 's', 1 by 'p', 2 by 'd', 3 by 'f', and 4 by 'g'. For instance, onemay speak of the subshell with n = 2 and as a '2s subshell'.

The shapes of orbitalsAny discussion of the shapes of electron orbitals is



The shapes of the first five atomic orbitals: 1s, 2s,2px,2py, and 2pz. The colors show the

wavefunction phase.

necessarily imprecise, because a given electron, regardlessof which orbital it occupies, can at any moment be found atany distance from the nucleus and in any direction due to theuncertainty principle.

However, the electron is much more likely to be found incertain regions of the atom than in others. Given this, aboundary surface can be drawn so that the electron has ahigh probability to be found anywhere within the surface,and all regions outside the surface have low values. The precise placement of the surface is arbitrary, but anyreasonably compact determination must follow a pattern specified by the behavior of ψ2, the square of thewavefunction. This boundary surface is what is meant when the "shape" of an orbital is referred to.

Generally speaking, the number n determines the size and energy of the orbital for a given nucleus: as n increases,the size of the orbital increases. However, in comparing different elements, the higher nuclear charge Z of heavierelements causes their orbitals to contract by comparison to lighter ones, so that the overall size of the whole atomremains very roughly constant, even as the number of electrons in heavier elements (higher Z) increases.

Also in general terms, determines an orbital's shape, and its orientation. However, since some orbitals aredescribed by equations in complex numbers, the shape sometimes depends on also.

The single s-orbitals ( ) are shaped like spheres. For n=1 the sphere is "solid" (it is most dense at the centerand fades exponentially outwardly), but for n=2 or more, each single s-orbital is composed of spherically symmetricsurfaces which are nested shells (i.e., the "wave-structure" is radial, following a sinusoidal radial component as well).The s-orbitals for all n numbers are the only orbitals with an anti-node (a region of high wave function density) atthe center of the nucleus. All other orbitals (p, d, f, etc.) have angular momentum, and thus avoid the nucleus(having a wave node at the nucleus).

The three p-orbitals for n=2 have the form of two ellipsoids with a point of tangency at the nucleus (sometimes

referred to as a dumbbell). The three p-orbitals in each shell are oriented at right angles to each other, asdetermined by their respective linear combination of values of .

Four of the five d-orbitals for n=3 look similar, each with four pear-shaped balls, each ball tangent to two others,

and the centers of all four lying in one plane, between a pair of axes. Three of these planes are the xy-, xz-, and

yz-planes, and the fourth has the centres on the x and y axes. The fifth and final d-orbital consists of three regions

of high probability density: a torus with two pear-shaped regions placed symmetrically on its z axis.

There are seven f-orbitals, each with shapes more complex than those of the d-orbitals.

For each s, p, d, f and g set of orbitals, the set of orbitals which composes it forms a spherically symmetrical set ofshapes. For non-s orbitals, which have lobes, the lobes point in directions so as to fill space as symmetrically aspossible for number of lobes which exist for a set of orientations. For example, the three p orbitals have six lobeswhich are oriented to each of the six primary directions of 3-D space; for the 5 d orbitals, there are a total of 18lobes, in which again six point in primary directions, and the 12 additional lobes fill the 12 gaps which exist betweeneach pairs of these 6 primary axes.

Additionally, as is the case with the s orbitals, individual p, d, f and g orbitals with n values higher than the lowestpossible value, exhibit an additional radial node structure which is reminiscent of harmonic waves of the same type,as compared with the lowest (or fundamental) mode of the wave. As with s orbitals, this phenomenon provides p,d, f, and g orbitals at the next higher possible value of n (for example, 3p orbitals vs. the fundamental 2p), anadditional node in each lobe. Still higher values of n further increase the number of radial nodes, for each type oforbital.

The shapes of atomic orbitals in one-electron atom are related to 3-dimensional spherical harmonics. Theseshapes are not unique, and any linear combination is valid, in fact it is possible to generate sets where all the d's



are the same shape, just like the px, py, and pz are the same shape.[10][11]

Orbitals table

This table shows all orbital configurations for the real hydrogen-like wave functions up to 7s, and therefore coversthe simple electronic configuration for all elements in the periodic table up to radium. It is should also be noted thatthe pz orbital is the same as the p0 orbital, but the px and py are formed by taking linear compbinations of the p+1and p-1 orbitals (which is why they are listed under the m=±1 label). Also, the p+1 and p-1 are not the same shapeas the p0, since they are pure spherical harmonics.

s (l=0) p (l=1) d (l=2) f (l=3)

m=0 m=0 m=±1 m=0 m=±1 m=±2 m=0 m=±1 m=±2 m=±3

s pz px py dz2 dxz dyz dxy dx2-y2 fz3 fxz2 fyz2 fxyzfz(x2-

y2)

fx(x2-3y2)

fy(3x2-y2)

n=1

n=2

n=3

n=4

n=5 . . . . . . . . . . . . . . . . . . . . .

n=6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

n=7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Orbital energyIn atoms with a single electron (hydrogen-like atoms), the energy of an orbital (and, consequently, of any electronsin the orbital) is determined exclusively by n. The n = 1 orbital has the lowest possible energy in the atom. Each

successively higher value of n has a higher level of energy, but the difference decreases as n increases. For high n,the level of energy becomes so high that the electron can easily escape from the atom.

In atoms with multiple electrons, the energy of an electron depends not only on the intrinsic properties of its orbital,but also on its interactions with the other electrons. These interactions depend on the detail of its spatial probabilitydistribution, and so the energy levels of orbitals depend not only on n but also on . Higher values of areassociated with higher values of energy; for instance, the 2p state is higher than the 2s state. When = 2, theincrease in energy of the orbital becomes so large as to push the energy of orbital above the energy of the s-orbitalin the next higher shell; when = 3 the energy is pushed into the shell two steps higher.

The energy sequence of the first 24 subshells is given in the following table. Each cell represents a subshell with nand given by its row and column indices, respectively. The number in the cell is the subshell's position in thesequence.

s p d f g



1 1

2 2 3

3 4 5 7

4 6 8 10 13

5 9 11 14 17 21

6 12 15 18 22 26

7 16 19 23 27 31

8 20 24 28 32 36

Note: empty cells indicate non-existent sublevels, while numbers in italics indicate sublevels that could exist,but which do not hold electrons in any element currently known.

Electron placement and the periodic tableSeveral rules govern the placement of electrons in orbitals (electron configuration). The first dictates that no twoelectrons in an atom may have the same set of values of quantum numbers (this is the Pauli exclusion principle).These quantum numbers include the three that define orbitals, as well as s, or spin quantum number. Thus, twoelectrons may occupy a single orbital, so long as they have different values of s. However, only two electrons,because of their spin, can be associated with each orbital.

Additionally, an electron always tends to fall to the lowest possible energy state. It is possible for it to occupy anyorbital so long as it does not violate the Pauli exclusion principle, but if lower-energy orbitals are available, thiscondition is unstable. The electron will eventually lose energy (by releasing a photon) and drop into the lowerorbital. Thus, electrons fill orbitals in the order specified by the energy sequence given above.

This behavior is responsible for the structure of the periodic table. The table may be divided into several rows(called 'periods'), numbered starting with 1 at the top. The presently known elements occupy seven periods. If acertain period has number i, it consists of elements whose outermost electrons fall in the ith shell.

The periodic table may also be divided into several numbered rectangular 'blocks'. The elements belonging to agiven block have this common feature: their highest-energy electrons all belong to the same -state (but the nassociated with that -state depends upon the period). For instance, the leftmost two columns constitute the 's-block'. The outermost electrons of Li and Be respectively belong to the 2s subshell, and those of Na and Mg to the3s subshell.

The number of electrons in a neutral atom increases with the atomic number. The electrons in the outermost shell, orvalence electrons, tend to be responsible for an element's chemical behavior. Elements that contain the samenumber of valence electrons can be grouped together and display similar chemical properties.

Relativistic effects

Main article: Relativistic quantum chemistry

For elements with high atomic number Z, the effects of relativity become more pronounced, and especially so for selectrons, which move at relativistic velocities as they penetrate the screening electrons near the core of high Zatoms. This relativistic increase in momentum for high speed electrons causes a corresponding decrease inwavelength and contraction of 6s orbitals relative to 5d orbitals (by comparison to corresponding s and d electronsin lighter elements in the same column of the periodic table); this results in 6s valence electrons becoming lowered inenergy.

Examples of significant physical outcomes of this effect include the lowered melting temperature of mercury (whichresults from 6s electrons not being available for metal bonding) and the golden color of gold and caesium (whichresults from narrowing of 6s to 5d transition energy to the point that visible light begins to be absorbed). See [1](http://www.chem1.com/acad/webtut/atomic/qprimer/#Q26) .

In the Bohr Model, an n = 1 electron has a velocity given by v = Zαc, where Z is the atomic number, α is the



fine-structure constant, and c is the speed of light. In non-relativistic quantum mechanics, therefore, any atom withan atomic number greater than 137 would require its 1s electrons to be traveling faster than the speed of light. Evenin the Dirac equation, which accounts for relativistic effects, the wavefunction of the electron for atoms with Z > 137is oscillatory and unbound. The significance of element 137, also known as untriseptium, was first pointed out by thephysicist Richard Feynman. Element 137 is sometimes informally called feynmanium (symbol Fy). However,Feynman's approximation fails to predict the exact critical value of Z due to the non-point-charge nature of thenucleus and very small orbital radius of inner electrons, resulting in a potential seen by inner electrons which iseffectively less than Z. The critical Z value which makes the atom unstable with regard to high-field breakdown ofthe vacuum and production of electron-positron pairs, does not occur until Z is about 173. These conditions are notseen except transiently in collisions of very heavy nuclei such as lead or uranium in accelerators, where suchelectron-positron production from these effects has been claimed to be observed. See Extension of the periodictable beyond the seventh period.

See alsoAtomic electron configuration tableElectron configurationEnergy levelList of Hund's rulesMolecular orbitalQuantum chemistry computer programs

References1. ^ Milton Orchin,Roger S. Macomber, Allan Pinhas, and R. Marshall Wilson(2005)"Atomic Orbital Theory

(http://media.wiley.com/product_data/excerpt/81/04716802/0471680281.pdf) "2. ^ Daintith, J. (2004). Oxford Dictionary of Chemistry. New York: Oxford University Press. ISBN 0-19-

860918-3.3. ^ The Feynman Lectures on Physics -The Definitive Edition, Vol 1 lect 6 pg 11. Feynman, Richard;

Leighton; Sands. (2006) Addison Wesley ISBN 0-8053-9046-44. ^ Bohr, Niels (1913). "On the Constitution of Atoms and Molecules". Philosophical Magazine 26 (1): 476.5. ^ Nagaoka, Hantaro (May 1904). "Kinetics of a System of Particles illustrating the Line and the Band

Spectrum and the Phenomena of Radioactivity" (http://www.chemteam.info/Chem-History/Nagaoka-1904.html) . Philosophical Magazine 7: 445–455. http://www.chemteam.info/Chem-History/Nagaoka-1904.html.

6. ^ Bryson, Bill (2003). A Short History of Nearly Everything. Broadway Books. pp. 141–143. ISBN 0-7679-0818-X.

7. ^ Mulliken, Robert S. (July 1932). "Electronic Structures of Polyatomic Molecules and Valence. II. GeneralConsiderations" (http://prola.aps.org/abstract/PR/v41/i1/p49_1) . Phys. Rev. 41 (1): 49–71.doi:10.1103/PhysRev.41.49 (http://dx.doi.org/10.1103%2FPhysRev.41.49) .http://prola.aps.org/abstract/PR/v41/i1/p49_1.

8. ^ Griffiths, David (1995). Introduction to Quantum Mechanics. Prentice Hall. pp. 190–191. ISBN 0-13-124405-1.

9. ^ Levine, Ira (2000). Quantum Chemistry (5 ed.). Prentice Hall. pp. 144–145. ISBN 0-13-685512-1.10. ^ Powell, Richard E. (1968). "The five equivalent d orbitals". Journal of Chemical Education 45: 45.

doi:10.1021/ed045p45 (http://dx.doi.org/10.1021%2Fed045p45) .11. ^ Kimball, George E. (1940). "Directed Valence". The Journal of Chemical Physics 8: 188.

doi:10.1063/1.1750628 (http://dx.doi.org/10.1063%2F1.1750628) .

Further readingTipler, Paul; Ralph Llewellyn (2003). Modern Physics (4 ed.). New York: W. H. Freeman and Company.ISBN 0-7167-4345-0.Scerri, Eric (2007). The Periodic Table, Its Story and Its Significance. New York: Oxford UniversityPress. ISBN 978-0-19-530573-9.

External links



Guide to atomic orbitals (http://www.chemguide.co.uk/atoms/properties/atomorbs.html)Covalent Bonds and Molecular Structure(http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_07.html)Animation of the time evolution of an hydrogenic orbital (http://strangepaths.com/atomic-orbital/2008/04/20/en/)The Orbitron (http://www.shef.ac.uk/chemistry/orbitron/) , a visualization of all common and uncommonatomic orbitals, from 1s to 7gGrand table (http://www.orbitals.com/orb/orbtable.htm) Still images of many orbitalsDavid Manthey's Orbital Viewer (http://www.orbitals.com/orb/index.html) renders orbitals with n ≤ 30Java orbital viewer applet (http://www.falstad.com/qmatom/)What does an atom look like? Orbitals in 3D(http://www.hydrogenlab.de/elektronium/HTML/einleitung_hauptseite_uk.html)

Atom Orbitals v.1.5 visualization software (http://taras-zavedy.narod.ru/PROGRAMMS/ATOM_ORBITALS_v_1_5_ENG/Atom_Orbitals_v_1_5_ENG.html)

Retrieved from "http://en.wikipedia.org/wiki/Atomic_orbital"Categories: Introductory physics | Quantum chemistry | Electron | Chemical bonding | Atomic physics

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