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## Atomic orbitalAn
Classically, the electrons were thought to orbit the atomic nucleus, much like the planets around the Sun (or more accurately, a moth orbiting very quickly around a lamp). Explaining the behavior of the electrons that "orbit" an atom was one of the driving forces behind the development of quantum mechanics. In quantum mechanics, atomic orbitals are described as wave functions over space, indexed by the The orbital names (s, p, d, f, g, h,...) are derived from the characteristics of their spectroscopic lines:
## Orbital namesOrbitals are given names in the form: where For example, the orbital 1 ## Formal quantum mechanical definitionIn quantum mechanics, the state of an atom, i.e. the eigenstates of the atomic Hamiltonian, is expanded (see configuration 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 called In atomic physics, the atomic spectral lines correspond to transitions (quantum leaps) between quantum states of an atom. 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 This notation means that the corresponding Slater determinants have a clear higher weight in the configuration interaction expansion. The atomic orbital concept is therefore a key concept for visualizing the excitation process associated to a given transition. For example, one can say for a given transition that it corresponds to the excitation of an electron from an occupied orbital to a given unoccupied orbital. Nevertheless one has to keep in mind that electrons are fermions ruled by Pauli exclusion principle and cannot be distinguished from the other electrons in the atom. Moreover, it sometimes happens that the configuration interaction expansion converges very slowly and that one cannot speak about simple one-determinantal wave function at all. This is the case when electron correlation is large. Fundamentally, an atomic orbital is a one-electron wavefunction. Don't forget that when thinking about orbitals, we are often bombarded (even if we don't know it) by the Hartree-Fock vision of molecular orbital theory. ## Connection to uncertainty relationAfter Heisenberg discovered his rightly famous uncertainty relation it was discovered by men like Pauling amd Mulliken that the consequences were that the electron could no longer be considered as in an exact location in its orbital. Rather the electron had to be described by every point where the electron could possibly inhabit. By creating points of probable location for the electron in its known orbital, this created a cloud of points in a spherical shape for the orbital of a hydrogen atom which points gradually faded out nearer to the nucleus and farther from the nucleus. This is called a probability distribution. Therefore, the Bohr atom number This led to the further description by Heisenberg that if a measurement of the electron was not being taken that it could not be described in one particular location but was everywhere in the electron cloud at once. In other words, quantum mechanics cannot give exact results, but only the probabilities for the occurrence of a variety of possible results. Heisenberg went further and said that the path of a moving particle only comes into existence once we observe it. However strange and counter-intuitive this assertion may seem, quantum mechanics does still tell us the location of the electron's orbital, its probability cloud. Heisenberg was speaking of the particle itself, not its orbital which is in a known probability distribution. It is important to note that although Heisenberg used infinite sets of positions for the electron in his matrices, this does not mean that the electron could be anywhere in the universe. Rather there are several laws that show the electron must be in one localized probability distribution. An electron is described by its energy in Bohr's atom which was carried over to matrix mechanics. Therefore, an electron in a certain n-sphere had to be within a certain range from the nucleus depending upon its energy. This restricts its location. Also, the number of places an electron can be is also called "the number of cells in its phase space". The Uncertainty Principle set a lower limit to how finely one can chop up classical phase space, so the number of places that an electron can be in its orbital becomes finite. An electron's location in an atom is defined to be in its orbital, but stops at the nucleus and before the next n-sphere orbital begins ## Hydrogen-like atomsThe simplest atomic orbitals are those that occur in an atom with a single electron, such as the hydrogen atom. In this case the atomic orbitals are the eigenstates of the hydrogen Hamiltonian. They can be obtained analytically (see hydrogen atom). An atom of any other element ionized down to a single electron is very similar to hydrogen, and the orbitals take the same form. For atoms with two or more electrons, the governing equations can only be solved with the use of methods of iterative approximation. Orbitals of multi-electron atoms are A given (hydrogen-like) atomic orbital is identified by unique values of three quantum numbers: The stationary states (quantum states) of the hydrogen-like atoms are its atomic orbital. However, in general, an electron'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 orbital method. The quantum number ## Qualitative characterization## Limitations on the quantum numbersAn atomic orbital is uniquely identified by the values of the three quantum numbers, and each set of the three quantum numbers corresponds to exactly one orbital, but the quantum numbers only occur in certain combinations of values. The rules governing the possible values of the quantum numbers are as follows: The principal quantum number The azimuthal quantum number is a non-negative integer. Within a shell where 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.
Subshells are usually identified by their ## The shapes of orbitalsAny discussion of the shapes of electron orbitals is necessarily imprecise, because a given electron, regardless of which orbital it occupies, can at any moment be found at any distance from the nucleus and in any direction due to the uncertainty principle. However, the electron is much more likely to be found in certain regions of the atom than in others. Given this, a Generally speaking, the number Also in general terms, determines an orbital's shape, and its orientation. However, since some orbitals are described by equations in complex numbers, the shape sometimes depends on also. The single The three Four of the five There are seven The shapes of atomic orbitals in one-electron atom are related to 3-dimensional spherical harmonics. ## Orbitals tableThis table shows all orbital configurations up to 7
## Orbital energyIn atoms with a single electron (essentially the hydrogen atom), the energy of an orbital (and, consequently, of any electrons in the orbital) is determined exclusively by 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 probability distribution, and so the energy levels of orbitals depend not only on The energy sequence of the first 24 subshells is given in the following table. Each cell represents a subshell with
## Electron placement and the periodic tableSeveral rules govern the placement of electrons in orbitals ( Additionally, an electron always tends to fall to the lowest possible energy state. It is possible for it to occupy any orbital so long as it does not violate the Pauli exclusion principle, but if lower-energy orbitals are available, this condition is unstable. The electron will eventually lose energy (by releasing a photon) and drop into the lower orbital. 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 a certain period has number The periodic table may also be divided into several numbered rectangular 'blocks'. The elements belonging to a given block have this common feature: their highest-energy electrons all belong to the same -state (but the The number of electrons in a neutral atom increases with the atomic number. The electrons in the outermost shell, or ## See also- List of Hund's rules
- Electron configuration
- Atomic electron configuration table
- Molecular orbital
- Energy level
## References**^**Daintith, J. (2004).*Oxford Dictionary of Chemistry*. New York: Oxford University Press.__ISBN 0-19-860918-3__.
- Tipler, Paul; Ralph Llewellyn (2003).
*Modern Physics*, 4, New York: W. H. Freeman and Company.__ISBN 0-7167-4345-0__.
Categories: Chemical bonding | Atomic physics |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Atomic_orbital". A list of authors is available in Wikipedia. |