Electron Configuration

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Electron configuration In atomic physics and quantum chemistry, electron configuration is the arrangement of electrons of an atom, a molecule, or other physical structure.[1] It concerns the way electrons can be distributed in the orbitals of the given system (atomic or molecular for instance). Like other elementary particles, the electron is subject to the laws ofquantum mechanics, and exhibits both particle-like and wave-like nature. Formally, the quantum state of a particular electron is defi
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  Electron configuration Inatomic physicsandquantum chemistry,  electron configuration is the arrangementof electronsof anatom, amolecule, or other physical structure. [1] It concerns the way electronscan be distributed in the orbitals of the given system (atomicormolecularfor instance). Like otherelementary particles, the electron is subject to the laws of quantum mechanics, and exhibits both particle-like and wave-like nature. Formally, thequantum stateof a particularelectron is defined by itswave function,acomplex-valuedfunction of space and time. According to theCopenhagen interpretationof quantum mechanics, the position of a particularelectron is not well defined until an act of measurementcauses it to be detected. Theprobability that the act of measurement will detect the electron at a particular point in space isproportional to the square of theabsolute valueof the wavefunction at that point.An energy is associated with each electron configuration and, upon certain conditions,electrons are able to move from one orbital to another by emission or absorption of aquantumof energy, in the form of aphoton. Knowledge of the electron configuration of different atoms is useful in understanding thestructure of theperiodic tableof elements. The concept is also useful for describing thechemical bonds that hold atoms together. In bulk materials this same idea helps explain thepeculiar properties of lasersandsemiconductors. Shells and subshells Electron configuration tableElectron configuration was first conceived of under theBohr modelof the atom, and it is stillcommon to speak of shells and subshells despite the advances in understanding of thequantum-mechanicalnature of electrons.An electron shell is the set of allowed stateselectrons may occupy which share thesameprincipal quantum number, n (the number before the letter in the orbital label). Anatom's n th electron shell can accommodate 2 n 2 electrons, e.g. the first shell can accommodate2 electrons, the second shell 8 electrons, and the third shell 18 electrons. The factor of twoarises because the allowed states are doubled due toelectron spin—eachatomic orbitaladmits up to two otherwise identical electrons with opposite spin, one with a spin +1/2(usually noted by an up-arrow) and one with a spin -1/2 (with a down-arrow).A subshell is the set of states defined by a commonazimuthal quantum number, l , within ashell. The values l = 0, 1, 2, 3 correspond to the s ,  p , d  , and f  labels, respectively. Themaximum number of electrons which can be placed in a subshell is given by 2(2 l + 1). Thisgives two electrons in an s subshell, six electrons in a p subshell, ten electrons in a d subshelland fourteen electrons in an f subshell. The numbers of electrons that can occupy each shell and each subshell arise from theequations of quantum mechanics, [2] in particular the Pauli exclusion principle, which states thatno two electrons in the same atom can have the same values of the fourquantum numbers. [3] [edit]Notation See also: Atomic orbital Physicists and chemists use a standard notation to indicate the electron configurations of atoms and molecules. For atoms, the notation consists of a sequence of atomic orbital labels(e.g. for phosphorus the sequence 1s, 2s, 2p, 3s, 3p) with the number of electrons assigned toeach orbital (or set of orbitals sharing the same label) placed as a superscript. Forexample,hydrogenhas one electron in the s-orbital of the first shell, so its configuration iswritten 1s 1 .Lithiumhas two electrons in the 1s-subshell and one in the (higher-energy) 2s-subshell, so its configuration is written 1s 2 2s 1 (pronounced one-s-two, two-s-one ).Phosphorus(atomic number15), is as follows: 1s 2 2s 2 2p 6 3s 2 3p 3 .For atoms with many electrons, this notation can become lengthy and so an abbreviatednotation is used, since all but the last few subshells are identical to those of one or another of thenoble gases. Phosphorus, for instance, differs fromneon(1s 2 2s 2 2p 6 ) only by the presenceof a third shell. Thus, the electron configuration of neon is pulled out, and phosphorus is  written as follows: [Ne] 3s 2 3p 3 . This convention is useful as it is the electrons in the outermostshell which most determine the chemistry of the element. The order of writing the orbitals is not completely fixed: some sources group all orbitals withthe same value of  n together, while other sources (as here) follow the order givenbyMadelung's rule. Hence the electron configuration of ironcan be written as [Ar] 3d 6 4s 2 (keeping the 3d-electrons with the 3s- and 3p-electrons which are implied by theconfiguration of argon) or as [Ar] 4s 2 3d 6 (following the Aufbau principle, see below). The superscript 1 for a singly-occupied orbital is not compulsory. [4]  It is quite common to seethe letters of the orbital labels (s, p, d, f) written in an italic or slanting typeface, althoughtheInternational Union of Pure and Applied Chemistry(IUPAC) recommends a normal typeface(as used here). The choice of letters srcinates from a now-obsolete system of categorizingspectral linesas sharp , principal , diffuse and fundamental , based on theirobservedfine structure: their modern usage indicates orbitals with anazimuthal quantum number, l , of 0, 1, 2 or 3 respectively. After f , the sequence continues alphabetically g , h , i ... ( l = 4, 5, 6...), skipping j , although orbitals of these types are rarely required. The electron configurations of molecules are written in a similar way, except thatmolecularorbitallabels are used instead of atomic orbital labels (see below). [edit]Energy — ground state and excited states  The energy associated to an electron is that of its orbital. The energy of a configuration is oftenapproximated as the sum of the energy of each electron, neglecting the electron-electroninteractions. The configuration that corresponds to the lowest electronic energy is calledtheground state. Any other configuration is anexcited state. As an example, the ground state configuration of thesodiumatom is 1s 2 2s 2 2p 6 3s, as deducedfrom the Aufbau principle (see below). The first excited state is obtained by promoting a 3selectron to the 3p orbital, to obtain the 1s 2 2s 2 2p 6 3p configuration, abbreviated as the 3p level.Atoms can move from one configuration to another by absorbing or emitting energy. Inasodium-vapor lampfor example, sodium atoms are excited to the 3p level by an electricaldischarge, and return to the ground state by emitting yellow light of wavelength 589 nm.Usually the excitation of valence electrons(such as 3s for sodium) involves energiescorresponding tophotonsof visible orultravioletlight. The excitation of core electronsis possible, but requires much higher energies generally corresponding tox-rayphotons. Thiswould be the case for example to excite a 2p electron to the 3s level and form the excited1s 2 2s 2 2p 5 3s 2 configuration. The remainder of this article deals only with the ground-state configuration, often referred toas the configuration of an atom or molecule. [edit]History Niels Bohrwas the first to propose (1923) that theperiodicityin the properties of the elements might be explained by the electronic structure of the atom. [5] His proposals were based on thethen currentBohr modelof the atom, in which the electron shells were orbits at a fixeddistance from the nucleus. Bohr's srcinal configurations would seem strange to a present-daychemist:sulfurwas given as 2.4.4.6 instead of 1s 2 2s 2 2p 6 3s 2 3p 4 (2.8.6). The following year,E. C. StonerincorporatedSommerfeld'sthird quantum number into the description of electron shells, and correctly predicted the shell structure of sulfur to be 2.8.6. [6]  However neither Bohr's system nor Stoner's could correctly describe the changes inatomicspectrain amagnetic field(theZeeman effect). Bohr was well aware of this shortcoming (and others), and had written to his friendWolfgangPaulito ask for his help in saving quantum theory (the system now known as old quantumtheory ). Pauli realized that the Zeeman effect must be due only to the outermost electrons of the atom, and was able to reproduce Stoner's shell structure, but with the correct structure of subshells, by his inclusion of a fourth quantum number and hisexclusion principle(1925): [7] It should be forbidden for more than one electron with the same value of the main quantumnumber  n to have the same value for the other three quantum numbers k [  l  ], j [  m l  ] and  m [  m s  ].   TheSchrödinger equation, published in 1926, gave three of the four quantum numbers as adirect consequence of its solution for the hydrogen atom: [2] this solution yields the atomicorbitals which are shown today in textbooks of chemistry (and above). The examination of atomic spectra allowed the electron configurations of atoms to be determined experimentally,and led to an empirical rule (known as Madelung's rule (1936), [8] see below) for the order inwhich atomic orbitals are filled with electrons. [edit]Aufbau principle and Madelung rule  TheAufbau principle(from theGerman   Aufbau , building up, construction ) was an importantpart of Bohr's srcinal concept of electron configuration. It may be stated as: [9] a maximum of two electrons are put into orbitals in the order of increasing orbital energy: thelowest-energy orbitals are filled before electrons are placed in higher-energy orbitals.  The approximate order of filling of atomic orbitals, following the arrows. The principle works very well (for the ground states of the atoms) for the first 18 elements,then decreasingly well for the following 100 elements. The modern form of the Aufbauprinciple describes an order of orbital energies given by Madelung's rule (or Klechkowski'srule). This rule was first stated byCharles Janetin 1929, rediscovered byErwin Madelungin 1936, [8] and later given a theoretical justification byV.M. Klechkowski [10] 1. Orbitals are filled in the order of increasing n + l ; 2. Where two orbitals have the same value of  n + l , they are filled in orderof increasing n . This gives the following order for filling the orbitals:1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, and 7p The Aufbau principle can be applied, in a modified form, to theprotonsandneutronsin theatomic nucleus, as in theshell modelof nuclear physicsandnuclear chemistry. The periodic table  The form of theperiodic tableis closely related to the electron configuration of the atoms of the elements. For example, all the elements of group 2have an electron configuration of [E] n s 2 (where [E] is an inert gas configuration), and have notable similarities in their chemicalproperties. The outermost electron shell is often referred to as the valence shell and (to afirst approximation) determines the chemical properties. It should be remembered that thesimilarities in the chemical properties were remarked more than a century before the idea of electron configuration, [11] It is not clear how far Madelung's rule explains (rather than simplydescribes) the periodic table, [12]  although some properties (such as the common +2oxidationstatein the first row of the transition metals) would obviously be different with a differentorder of orbital filling. Shortcomings of the Aufbau principle  The Aufbau principle rests on a fundamental postulate that the order of orbital energies isfixed, both for a given element and between different elements: neither of these is true(although they are approximately true enough for the principle to be useful). It considersatomic orbitals as boxes of fixed energy into which can be placed two electrons and no more.However the energy of an electron in an atomic orbital depends on the energies of all theother electrons of the atom (or ion, or molecule, etc.). There are no one-electron solutions forsystems of more than one electron, only a set of many-electron solutions which cannot becalculated exactly [13] (although there are mathematical approximations available, suchtheHartree–Fock method). The fact that the Aufbau principle is based on an approximation can be seen from the fact thatthere is an almost-fixed filling order at all, that, within a given shell, the s-orbital is alwaysfilled before the p-orbitals. In ahydrogen-like atom, which only has one electron, the s-orbitaland the p-orbitals of the same shell have exactly the same energy, to a very goodapproximation in the absence of external electromagnetic fields. (However, in a real hydrogenatom, the energy levels are slightly split by the magnetic field of the nucleus, and bythequantum electrodynamiceffects of theLamb shift).
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