In
atomic physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...
, a term symbol is an abbreviated description of the total spin and orbital
angular momentum quantum number
In quantum mechanics, the azimuthal quantum number is a quantum number for an atomic orbital that determines its angular momentum operator, orbital angular momentum and describes aspects of the angular shape of the orbital. The azimuthal quantum ...
s of the electrons in a multi-electron
atom
Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...
. So while the word ''symbol'' suggests otherwise, it represents an actual ''value'' of a
physical quantity
A physical quantity (or simply quantity) is a property of a material or system that can be Quantification (science), quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ''nu ...
.
For a given
electron configuration
In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon ato ...
of an atom, its state depends also on its total angular momentum, including spin and orbital components, which are specified by the term symbol. The usual atomic term symbols assume
LS coupling (also known as Russell–Saunders coupling) in which the all-electron total quantum numbers for orbital (''L''), spin (''S'') and total (''J'') angular momenta are
good quantum numbers.
In the terminology of
atomic spectroscopy
In physics, atomic spectroscopy is the study of the electromagnetic radiation absorbed and emitted by atoms. Since unique elements have unique emission spectra, atomic spectroscopy is applied for determination of elemental compositions. It can ...
, ''L'' and ''S'' together specify a term; ''L'', ''S'', and ''J'' specify a level; and ''L'', ''S'', ''J'' and the magnetic quantum number ''M''
''J'' specify a state. The conventional term symbol has the form
2''S''+1''L''
''J'', where ''J'' is written optionally in order to specify a level. ''L'' is written using
spectroscopic notation
Spectroscopic notation provides a way to specify atomic ionization states, atomic orbitals, and molecular orbitals.
Ionization states
Spectroscopists customarily refer to the spectrum arising from a given ionization state of a given element by ...
: for example, it is written "S", "P", "D", or "F" to represent ''L'' = 0, 1, 2, or 3 respectively. For coupling schemes other that LS coupling, such as the
jj coupling
In quantum mechanics, angular momentum coupling is the procedure of constructing eigenstates of total angular momentum out of eigenstates of separate angular momenta. For instance, the orbit and spin of a single particle can interact through sp ...
that applies to some heavy elements, other notations are used to specify the term.
Term symbols apply to both neutral and charged atoms, and to their ground and excited states. Term symbols usually specify the total for all electrons in an atom, but are sometimes used to describe electrons in a given
subshell or set of subshells, for example to describe each
open subshell in an atom having more than one. The
ground state
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state ...
term symbol for neutral atoms is described, in most cases, by
Hund's rules. Neutral atoms of the chemical elements have the same term symbol ''for each column'' in the
s-block and p-block elements, but differ in d-block and f-block elements where the ground-state electron configuration changes within a column, where exceptions to Hund's rules occur. Ground state term symbols for the chemical elements are given
below
Below may refer to:
*Earth
*Ground (disambiguation)
*Soil
*Floor
* Bottom (disambiguation)
*Less than
*Temperatures below freezing
*Hell or underworld
People with the surname
* Ernst von Below (1863–1955), German World War I general
* Fred Belo ...
.
Term symbols are also used to describe angular momentum quantum numbers for
atomic nuclei
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the University of Manchester based on the 1909 Geiger–Marsden gold foil experiment. Aft ...
and for molecules. For
molecular term symbols, Greek letters are used to designate the component of orbital angular momenta along the molecular axis.
The use of the word ''term'' for an atom's electronic state is based on the
Rydberg–Ritz combination principle, an empirical observation that the wavenumbers of spectral lines can be expressed as the difference of two ''terms''. This was later summarized by the
Bohr model
In atomic physics, the Bohr model or Rutherford–Bohr model was a model of the atom that incorporated some early quantum concepts. Developed from 1911 to 1918 by Niels Bohr and building on Ernest Rutherford's nuclear Rutherford model, model, i ...
, which identified the terms with quantized energy levels, and the spectral wavenumbers of these levels with photon energies.
Tables of atomic energy levels identified by their term symbols are available for atoms and ions in ground and excited states from the
National Institute of Standards and Technology
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into Outline of p ...
(NIST).
[
]
Term symbols with ''LS'' coupling
The usual atomic term symbols assume LS coupling (also known as Russell–Saunders coupling), in which the atom's total spin quantum number ''S'' and the total orbital angular momentum quantum number ''L'' are " good quantum numbers". (Russell–Saunders coupling is named after Henry Norris Russell and Frederick Albert Saunders, who described it in 1925). The spin-orbit interaction then couples the total spin and orbital moments to give the total electronic angular momentum quantum number ''J''. Atomic states are then well described by term symbols of the form:
where
- ''S'' is the total
spin quantum number
In physics and chemistry, the spin quantum number is a quantum number (designated ) that describes the intrinsic angular momentum (or spin angular momentum, or simply ''spin'') of an electron or other particle. It has the same value for all ...
for the atom's electrons. The value 2''S'' + 1 written in the term symbol is the spin multiplicity
Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. Spin is quantized, and accurate models for the interaction with spin require relativistic qu ...
, which is the number of possible values of the spin magnetic quantum number ''MS'' for a given spin ''S''.
- ''J'' is the total angular momentum quantum number for the atom's electrons. ''J'' has a value in the range from , ''L'' − ''S'', to ''L'' + ''S''.
- ''L'' is the total orbital quantum number in
spectroscopic notation
Spectroscopic notation provides a way to specify atomic ionization states, atomic orbitals, and molecular orbitals.
Ionization states
Spectroscopists customarily refer to the spectrum arising from a given ionization state of a given element by ...
, in which the symbols for ''L'' are:
The orbital symbols S, P, D and F are derived from the characteristics of the spectroscopic lines corresponding to s, p, d, and f orbitals: sharp, principal, diffuse
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
, and fundamental; the rest are named in alphabetical order from G onwards (omitting J, S and P). When used to describe electronic states of an atom, the term symbol is often written following the electron configuration
In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon ato ...
. For example, 1s22s22p2 3P0 represents the ground state of a neutral carbon
Carbon () is a chemical element; it has chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetravalent—meaning that its atoms are able to form up to four covalent bonds due to its valence shell exhibiting 4 ...
atom. The superscript 3 indicates that the spin multiplicity 2''S'' + 1 is 3 (it is a triplet state
In quantum mechanics, a triplet state, or spin triplet, is the quantum state of an object such as an electron, atom, or molecule, having a quantum spin ''S'' = 1. It has three allowed values of the spin's projection along a given axis ''m''S = � ...
), so ''S'' = 1; the letter "P" is spectroscopic notation for ''L'' = 1; and the subscript 0 is the value of ''J'' (in this case ''J'' = ''L'' − ''S'').[NIST Atomic Spectrum Database]
For example, to display the levels for a neutral carbon atom, enter "C I" or "C 0" in the "Spectrum" box and click "Retrieve data".
Small letters refer to individual orbitals or one-electron quantum numbers, whereas capital letters refer to many-electron states or their quantum numbers.
Terminology: terms, levels, and states
For a given electron configuration,
* The combination of an value and an value is called a term, and has a statistical weight (i.e., number of possible states) equal to ;
* A combination of , and is called a level. A given level has a statistical weight of , which is the number of possible states associated with this level in the corresponding term;
* A combination of , , and determines a single state.
The product as a number of possible states with given ''S'' and ''L'' is also a number of basis states in the uncoupled representation, where '', '', '', '' ( and are z-axis components of total spin and total orbital angular momentum respectively) are good quantum numbers whose corresponding operators mutually commute. With given and , the eigenstates in this representation span function space of dimension , as and . In the coupled representation where total angular momentum (spin + orbital) is treated, the associated states (or eigenstates
In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system re ...
) are and these states span the function space with dimension of
as . Obviously, the dimension of function space in both representations must be the same.
As an example, for , there are different states (= eigenstates in the uncoupled representation) corresponding to the 3D ''term'', of which belong to the 3D3 (''J'' = 3) level. The sum of for all levels in the same term equals (2''S''+1)(2''L''+1) as the dimensions of both representations must be equal as described above. In this case, ''J'' can be 1, 2, or 3, so 3 + 5 + 7 = 15.
Term symbol parity
The parity of a term symbol is calculated as
where is the orbital quantum number for each electron. means even parity while is for odd parity. In fact, only electrons in odd orbitals (with odd) contribute to the total parity: an odd number of electrons in odd orbitals (those with an odd such as in p, f, ...) correspond to an odd term symbol, while an even number of electrons in odd orbitals correspond to an even term symbol. The number of electrons in even orbitals is irrelevant as any sum of even numbers is even. For any closed subshell, the number of electrons is which is even, so the summation of in closed subshells is always an even number. The summation of quantum numbers over open (unfilled) subshells of odd orbitals ( odd) determines the parity of the term symbol. If the number of electrons in this ''reduced'' summation is odd (even) then the parity is also odd (even).
When it is odd, the parity of the term symbol is indicated by a superscript letter "o", otherwise it is omitted:
Alternatively, parity may be indicated with a subscript letter "g" or "u", standing for ''gerade'' (German for "even") or ''ungerade'' ("odd"):
Ground state term symbol
It is relatively easy to predict the term symbol for the ground state of an atom using Hund's rules. It corresponds to a state with maximum ''S'' and ''L''.
#Start with the most stable electron configuration
In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon ato ...
. Full shells and subshells do not contribute to the overall angular momentum
Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total ang ...
, so they are discarded.
#*If all shells and subshells are full then the term symbol is 1S0.
#Distribute the electrons in the available orbitals, following the Pauli exclusion principle
In quantum mechanics, the Pauli exclusion principle (German: Pauli-Ausschlussprinzip) states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that o ...
.
#*Conventionally, put 1 electron into orbital with highest and then continue filling other orbitals in descending order with one electron each, until you are out of electrons, or all orbitals in the subshell have one electron. Assign, again conventionally, all these electrons a value + of quantum magnetic spin number .
#* If there are remaining electrons, put them in orbitals in the same order as before, but now assigning to them.
#The overall ''S'' is calculated by adding the ''ms'' values for each electron. The overall ''S'' is then times the number of unpaired electrons.
#The overall ''L'' is calculated by adding the values for each electron (so if there are two electrons in the same orbital, add twice that orbital's ).
#Calculate ''J'' as
#*if less than half of the subshell is occupied, take the minimum value ;
#*if more than half-filled, take the maximum value ;
#*if the subshell is half-filled, then ''L'' will be 0, so .
As an example, in the case of fluorine
Fluorine is a chemical element; it has Chemical symbol, symbol F and atomic number 9. It is the lightest halogen and exists at Standard temperature and pressure, standard conditions as pale yellow Diatomic molecule, diatomic gas. Fluorine is extre ...
, the electronic configuration is 1s22s22p5.
- Discard the full subshells and keep the 2p5 part. So there are five electrons to place in subshell p ().
- There are three orbitals () that can hold up to . The first three electrons can take but the Pauli exclusion principle forces the next two to have because they go to already occupied orbitals.
- ;
- , which is "P" in spectroscopic notation.
- As fluorine 2p subshell is more than half filled, . Its ground state term symbol is then .
Atomic term symbols of the chemical elements
In the periodic table, because atoms of elements in a column usually have the same outer electron structure, and always have the same electron structure in the "s-block" and "p-block" elements (see block (periodic table)
A block of the periodic table is a set of elements unified by the atomic orbitals their valence electrons or vacancies lie in. The term seems to have been first used by Charles Janet. Each block is named after its characteristic orbital: s-bl ...
), all elements may share the same ground state term symbol for the column. Thus, hydrogen and the alkali metal
The alkali metals consist of the chemical elements lithium (Li), sodium (Na), potassium (K),The symbols Na and K for sodium and potassium are derived from their Latin names, ''natrium'' and ''kalium''; these are still the origins of the names ...
s are all 2S, the alkaline earth metal
The alkaline earth metals are six chemical elements in group (periodic table), group 2 of the periodic table. They are beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra).. The elements have very similar p ...
s are 1S0, the boron column elements are 2P, the carbon column elements are 3P0, the pnictogen
, -
! colspan=2 style="text-align:left;" , ↓ Period
, -
! 2
,
, -
! 3
,
, -
! 4
,
, -
! 5
,
, -
! 6
,
, -
! 7
,
, -
, colspan="2",
----
''Legend''
A pnictogen ( or ; from "to choke" and -gen, "generator") is any ...
s are 4S, the chalcogen
The chalcogens (ore forming) ( ) are the chemical elements in group 16 of the periodic table. This group is also known as the oxygen family. Group 16 consists of the elements oxygen (O), sulfur (S), selenium (Se), tellurium (Te), and the rad ...
s are 3P2, the halogen
The halogens () are a group in the periodic table consisting of six chemically related elements: fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and the radioactive elements astatine (At) and tennessine (Ts), though some authors would ...
s are 2P, and the inert gas
An inert gas is a gas that does not readily undergo chemical reactions with other chemical substances and therefore does not readily form chemical compounds. Though inert gases have a variety of applications, they are generally used to prevent u ...
es are 1S0, per the rule for full shells and subshells stated above.
Term symbols for the ground states of most chemical elements are given in the collapsed table below. In the d-block and f-block, the term symbols are not always the same for elements in the same column of the periodic table, because open shells of several d or f electrons have several closely spaced terms whose energy ordering is often perturbed by the addition of an extra complete shell to form the next element in the column.
For example, the table shows that the first pair of vertically adjacent atoms with different ground-state term symbols are V and Nb. The 6D ground state of Nb corresponds to an excited state of V 2112 cm−1 above the 4F ground state of V, which in turn corresponds to an excited state of Nb 1143 cm−1 above the Nb ground state.[ These energy differences are small compared to the 15158 cm−1 difference between the ground and first excited state of Ca,][ which is the last element before V with no d electrons.
]
Term symbols for an electron configuration
The process to calculate all possible term symbols for a given electron configuration
In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon ato ...
is somewhat longer.
- First, the total number of possible states is calculated for a given electron configuration. As before, the filled (sub)shells are discarded, and only the partially filled ones are kept. For a given orbital quantum number , is the maximum allowed number of electrons, . If there are electrons in a given subshell, the number of possible states is
.
As an example, consider the
carbon
Carbon () is a chemical element; it has chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetravalent—meaning that its atoms are able to form up to four covalent bonds due to its valence shell exhibiting 4 ...
electron structure: 1s22s22p2. After removing full subshells, there are 2 electrons in a p-level (), so there are
=15
different states.
- Second, all possible states are drawn. ''ML'' and ''MS'' for each state are calculated, with where ''mi'' is either or for the ''i''-th electron, and ''M'' represents the resulting ''ML'' or ''MS'' respectively:
- Third, the number of states for each (''ML'',''MS'') possible combination is counted:
- Fourth, smaller tables can be extracted representing each possible term. Each table will have the size (2''L''+1) by (2''S''+1), and will contain only "1"s as entries. The first table extracted corresponds to ''ML'' ranging from −2 to +2 (so ), with a single value for ''MS'' (implying ). This corresponds to a 1D term. The remaining terms fit inside the middle 3×3 portion of the table above. Then a second table can be extracted, removing the entries for ''ML'' and ''MS'' both ranging from −1 to +1 (and so , a 3P term). The remaining table is a 1×1 table, with , i.e., a 1S term.
- Fifth, applying Hund's rules, the ground state can be identified (or the lowest state for the configuration of interest). Hund's rules should not be used to predict the order of states other than the lowest for a given configuration. (See examples at .)
- If only two equivalent electrons are involved, there is an "Even Rule" which states that, for two equivalent electrons, the only states that are allowed are those for which the sum (L + S) is even.
Case of three equivalent electrons
Alternative method using group theory
For configurations with at most two electrons (or holes) per subshell, an alternative and much quicker method of arriving at the same result can be obtained from group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...
. The configuration 2p2 has the symmetry of the following direct product in the full rotation group:
which, using the familiar labels , and , can be written as
The square brackets enclose the anti-symmetric square. Hence the 2p2 configuration has components with the following symmetries:
The Pauli principle and the requirement for electrons to be described by anti-symmetric wavefunctions imply that only the following combinations of spatial and spin symmetry are allowed:
Then one can move to step five in the procedure above, applying Hund's rules.
The group theory method can be carried out for other such configurations, like 3d2, using the general formula
The symmetric square will give rise to singlets (such as 1S, 1D, & 1G), while the anti-symmetric square gives rise to triplets (such as 3P & 3F).
More generally, one can use
where, since the product is not a square, it is not split into symmetric and anti-symmetric parts. Where two electrons come from inequivalent orbitals, both a singlet and a triplet are allowed in each case.
Summary of various coupling schemes and corresponding term symbols
Basic concepts for all coupling schemes:
* : individual orbital angular momentum vector for an electron, : individual spin vector for an electron, : individual total angular momentum vector for an electron, .
* : Total orbital angular momentum vector for all electrons in an atom ().
* : total spin vector for all electrons ().
* : total angular momentum vector for all electrons. The way the angular momenta are combined to form depends on the coupling scheme: for ''LS'' coupling, for ''jj'' coupling, etc.
* A quantum number corresponding to the magnitude of a vector is a letter without an arrow, or without boldface (example: ''ℓ'' is the orbital angular momentum quantum number for and )
* The parameter called multiplicity represents the number of possible values of the total angular momentum quantum number ''J'' for certain conditions.
* For a single electron, the term symbol is not written as ''S'' is always 1/2, and ''L'' is obvious from the orbital type.
* For two electron groups ''A'' and ''B'' with their own terms, each term may represent ''S'', ''L'' and ''J'' which are quantum numbers corresponding to the , and vectors for each group. "Coupling" of terms ''A'' and ''B'' to form a new term ''C'' means finding quantum numbers for new vectors , and . This example is for ''LS'' coupling and which vectors are summed in a coupling is depending on which scheme of coupling is taken. Of course, the angular momentum addition rule is that where ''X'' can be ''s'', ''ℓ'', ''j'', ''S'', ''L'', ''J'' or any other angular momentum-magnitude-related quantum number.
''LS'' coupling (Russell–Saunders coupling)
* Coupling scheme: and are calculated first then is obtained. From a practical point of view, it means ''L'', ''S'' and ''J'' are obtained by using an addition rule of the angular momenta of given electron groups that are to be coupled.
* Electronic configuration + Term symbol: . is a term which is from coupling of electrons in group. are principle quantum number, orbital quantum number and means there are ''N'' (equivalent) electrons in subshell. For , is equal to multiplicity, a number of possible values in ''J'' (final total angular momentum quantum number) from given ''S'' and ''L''. For , multiplicity is but is still written in the term symbol. Strictly speaking, is called ''level'' and is called ''term''. Sometimes right superscript ''o'' is attached to the term symbol, meaning the parity of the group is odd ().
* Example:
*# 3d7 4F7/2: 4F7/2 is level of 3d7 group in which are equivalent 7 electrons are in 3d subshell.
*# 3d7(4F)4s4p(3P0) 6F: Terms are assigned for each group (with different principal quantum number ''n'') and rightmost level 6F is from coupling of terms of these groups so 6F represents final total spin quantum number ''S'', total orbital angular momentum quantum number ''L'' and total angular momentum quantum number ''J'' in this atomic energy level. The symbols 4F and 3P''o'' refer to seven and two electrons respectively so capital letters are used.
*# 4f7(8S0)5d (7D''o'')6p 8F13/2: There is a space between 5d and (7D''o''). It means (8S0) and 5d are coupled to get (7D''o''). Final level 8F is from coupling of (7D''o'') and 6p.
*# 4f(2F0) 5d2(1G) 6s(2G) 1P: There is only one term 2F''o'' which is isolated in the left of the leftmost space. It means (2F''o'') is coupled lastly; (1G) and 6s are coupled to get (2G) then (2G) and (2F''o'') are coupled to get final term 1P.
''jj'' Coupling
* Coupling scheme: .
* Electronic configuration + Term symbol:
* Example:
*# : There are two groups. One is and the other is . In , there are 2 electrons having in 6p subshell while there is an electron having in the same subshell in . Coupling of these two groups results in (coupling of ''j'' of three electrons).
*# : in () is for 1st group and in () is ''J''2 for 2nd group . Subscript 11/2 of term symbol is final ''J'' of .
''J''1''L''2 coupling
* Coupling scheme: and .
* Electronic configuration + Term symbol: . For is equal to multiplicity, a number of possible values in ''J'' (final total angular momentum quantum number) from given ''S''2 and ''K''. For , multiplicity is but is still written in the term symbol.
* Example:
*# 3p5(2P)5g 2 /2 . is ''K'', which comes from coupling of ''J''1 and ''ℓ''2. Subscript 5 in term symbol is ''J'' which is from coupling of ''K'' and ''s''2.
*# 4f13(2F)5d2(1D) /2 . is ''K'', which comes from coupling of ''J''1 and ''L''2. Subscript in the term symbol is ''J'' which is from coupling of ''K'' and ''S''2.
''LS''1 coupling
* Coupling scheme:, .
* Electronic configuration + Term symbol: . For is equal to multiplicity, a number of possible values in ''J'' (final total angular momentum quantum number) from given ''S''2 and ''K''. For , multiplicity is but is still written in the term symbol.
* Example:
*# 3d7(4P)4s4p(3P''o'') D''o'' 3 /2 . .
Most famous coupling schemes are introduced here but these schemes can be mixed to express the energy state of an atom. This summary is based o
Racah notation and Paschen notation
These are notations for describing states of singly excited atoms, especially noble gas
The noble gases (historically the inert gases, sometimes referred to as aerogens) are the members of Group (periodic table), group 18 of the periodic table: helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), radon (Rn) and, in some ...
atoms. Racah notation is basically a combination of ''LS'' or Russell–Saunders coupling and ''J''1''L''2 coupling. ''LS'' coupling is for a parent ion and ''J''1''L''2 coupling is for a coupling of the parent ion and the excited electron. The parent ion is an unexcited part of the atom. For example, in Ar atom excited from a ground state ...3p6 to an excited state ...3p54p in electronic configuration, 3p5 is for the parent ion while 4p is for the excited electron.
In Racah notation, states of excited atoms are denoted as . Quantities with a subscript 1 are for the parent ion, and are principal and orbital quantum numbers for the excited electron, ''K'' and ''J'' are quantum numbers for and where and are orbital angular momentum and spin for the excited electron respectively. “''o''” represents a parity of excited atom. For an inert (noble) gas atom, usual excited states are where ''N'' = 2, 3, 4, 5, 6 for Ne, Ar, Kr, Xe, Rn, respectively in order. Since the parent ion can only be 2P1/2 or 2P3/2, the notation can be shortened to or , where means the parent ion is in 2P3/2 while is for the parent ion in 2P1/2 state.
Paschen notation is a somewhat odd notation; it is an old notation made to attempt to fit an emission spectrum of neon to a hydrogen-like theory. It has a rather simple structure to indicate energy levels of an excited atom. The energy levels are denoted as . is just an orbital quantum number of the excited electron. is written in a way that 1s for , 2p for , 2s for , 3p for , 3s for , etc. Rules of writing from the lowest electronic configuration of the excited electron are: (1) is written first, (2) is consecutively written from 1 and the relation of (like a relation between and ) is kept. is an attempt to describe electronic configuration of the excited electron in a way of describing electronic configuration of hydrogen atom. ''#'' is an additional number denoted to each energy level of given (there can be multiple energy levels of given electronic configuration, denoted by the term symbol). ''#'' denotes each level in order, for example, ''#'' = 10 is for a lower energy level than ''#'' = 9 level and ''#'' = 1 is for the highest level in a given . An example of Paschen notation is below.
{, class="wikitable"
!Electronic configuration of Neon
!
!Electronic configuration of Argon
!
, -
, 1s22s22p6
, ''Ground state''
, es23p6
, ''Ground state''
, -
, 1s22s22p53s1
, 1s
, es23p54s1
, 1s
, -
, 1s22s22p53p1
, 2p
, es23p54p1
, 2p
, -
, 1s22s22p54s1
, 2s
, es23p55s1
, 2s
, -
, 1s22s22p54p1
, 3p
, es23p55p1
, 3p
, -
, 1s22s22p55s1
, 3s
, es23p56s1
, 3s
See also
* Quantum number
In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system.
To fully specify the state of the electron in a hydrogen atom, four quantum numbers are needed. The traditional set of quantu ...
** Principal quantum number
In quantum mechanics, the principal quantum number (''n'') of an electron in an atom indicates which electron shell or energy level it is in. Its values are natural numbers (1, 2, 3, ...).
Hydrogen and Helium, at their lowest energies, have just ...
** Azimuthal quantum number
In quantum mechanics, the azimuthal quantum number is a quantum number for an atomic orbital that determines its angular momentum operator, orbital angular momentum and describes aspects of the angular shape of the orbital. The azimuthal quantum ...
** Spin quantum number
In physics and chemistry, the spin quantum number is a quantum number (designated ) that describes the intrinsic angular momentum (or spin angular momentum, or simply ''spin'') of an electron or other particle. It has the same value for all ...
** Magnetic quantum number
In atomic physics, a magnetic quantum number is a quantum number used to distinguish quantum states of an electron or other particle according to its angular momentum along a given axis in space. The orbital magnetic quantum number ( or ) disting ...
* Angular quantum numbers
* Angular momentum coupling
In quantum mechanics, angular momentum coupling is the procedure of constructing eigenstates of total angular momentum out of eigenstates of separate angular momenta. For instance, the orbit and spin of a single particle can interact through spi ...
* Molecular term symbol
Notes
References
{{DEFAULTSORT:Term Symbol
Atomic physics
Theoretical chemistry
Quantum chemistry