Aufbau principle

The aufbau principle states that in the ground state of an atom or ion, electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. For example, the 1s shell is filled before the 2s subshell is occupied. In this way, the electrons of an atom or ion form the most stable electron configuration possible. An example is the configuration 1s2 2s2 2p6 3s2 3p3 for the phosphorus atom, meaning that the 1s subshell has 2 electrons etc.

Aufbau is a German noun that means construction or "building-up". The aufbau principle is sometimes called the building-up principle or the aufbau rule.

The details of this "building-up" tendency are described mathematically by atomic orbital functions. Electron behavior is elaborated by other principles of atomic physics, such as Hund's rule and the Pauli exclusion principle. Hund's rule asserts that if multiple orbitals of the same energy are available, electrons will occupy different orbitals singly before any are occupied doubly. If double occupation does occur, the Pauli exclusion principle requires that electrons which occupy the same orbital must have different spins (+1/2 and −1/2).

As we pass from one element to another of next higher atomic number, one proton and one electron are added each time to the neutral atom. The maximum number of electrons in any shell is 2n2, where n is the principal quantum number. The maximum number of electrons in a subshell (s, p, d or f) is equal to 2(2ℓ+1) where ℓ = 0, 1, 2, 3... Thus these subshells can have a maximum of 2, 6, 10 and 14 electrons respectively. In the ground state the electronic configuration can be built up by placing electrons in the lowest available orbitals until the total number of electrons added is equal to the atomic number. Thus orbitals are filled in the order of increasing energy, using two general rules to help predict electronic configurations:

1. Electrons are assigned to orbitals in order of increasing value of (n+ℓ).
2. For subshells with the same value of (n+ℓ), electrons are assigned first to the sub shell with lower n.

A version of the aufbau principle known as the nuclear shell model is used to predict the configuration of protons and neutrons in an atomic nucleus.[1]

Madelung energy ordering rule

Aufbau Principle
The states crossed by same red arrow have same value. The direction of the red arrow indicates the order of state filling.

In neutral atoms, the order in which subshells are filled is given by the n + ℓ rule, also known as the Madelung rule (after Erwin Madelung), or the Janet rule or the Klechkowsky rule (after Charles Janet or Vsevolod Klechkovsky in some, mostly French and Russian-speaking, countries), or the diagonal rule.[2] Orbitals with a lower n + ℓ value are filled before those with higher n + ℓ values. In this context, n represents the principal quantum number and the azimuthal quantum number; the values = 0, 1, 2, 3 correspond to the s, p, d, and f labels, respectively. The subshell ordering by this rule is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, 8s, ... For example titanium (Z = 22) has the ground-state configuration 1s2 2s2 2p6 3s2 3p6 4s2 3d2 [3]

Other authors write the orbitals always in order of increasing n, such as Ti (Z = 22) 1s2 2s2 2p6 3s2 3p6 3d2 4s2.[4] This can be called "leaving order", since if the atom is ionized, electrons leave in the order 4s, 3d, 3p, 3s, etc. For a given neutral atom, the two notations are equivalent since only the orbital occupancies have physical significance.

The rule is based on the total number of nodes in the atomic orbital, n + ℓ, which is related to the energy.[5] In the case of equal n + ℓ values, the orbital with a lower n value is filled first. The fact that most of the ground state configurations of neutral atoms fill orbitals following this n + ℓ, n pattern was obtained experimentally, by reference to the spectroscopic characteristics of the elements.[6]

The Madelung energy ordering rule applies only to neutral atoms in their ground state. There are 10 elements among the transition metals and 9 elements among the lanthanides and actinides for which the Madelung rule predicts an electron configuration that differs from that determined experimentally by one electron orbit (in the case of palladium and thorium by two electron orbits).[7]

Exceptions to the Madelung rule in the transition metals:

The valence d-subshell "borrows" one electron (in the case of palladium two electrons) from the valence s-subshell.

Atom 24Cr 29Cu 41Nb 42Mo 44Ru 45Rh 46Pd 47Ag 78Pt 79Au
Core electrons [Ar] [Ar] [Kr] [Kr] [Kr] [Kr] [Kr] [Kr] [Xe] [Xe]
Madelung Rule 3d44s2 3d94s2 4d35s2 4d45s2 4d65s2 4d75s2 4d85s2 4d95s2 4f145d86s2 4f145d96s2
Experiment 3d54s1 3d104s1 4d45s1 4d55s1 4d75s1 4d85s1 4d10 4d105s1 4f145d96s1 4f145d106s1

Example copper 29Cu: According to the Madelung rule, the 4s orbital (n + ℓ = 4 + 0 = 4) is occupied before the 3d orbital (n + ℓ = 3 + 2 = 5). The rule then predicts the electron configuration 1s22s22p63s2 3p63d94s2, abbreviated [Ar]3d94s2 where [Ar] denotes the configuration of the preceding noble gas argon. However the measured electron configuration of the copper atom is [Ar]3d104s1. By filling the 3d orbital, copper can be in a lower energy state.

Exceptions to the Madelung rule in the lanthanides and actinides:

The valence d-subshell "borrows" one electron (in the case of thorium two electrons) from the valence f-subshell.

Atom 57La 58Ce 64Gd 89Ac 90Th 91Pa 92U 93Np 96Cm
Core electrons [Xe] [Xe] [Xe] [Rn] [Rn] [Rn] [Rn] [Rn] [Rn]
Madelung Rule 4f16s2 4f26s2 4f86s2 5f17s2 5f27s2 5f37s2 5f47s2 5f57s2 5f87s2
Experiment 5d16s2 4f15d16s2 4f75d16s2 6d17s2 6d27s2 5f26d17s2 5f36d17s2 5f46d17s2 5f76d17s2

Example uranium 92U: According to the Madelung rule, the 5f orbital (n + ℓ = 5 + 3 = 8) is occupied before the 6d orbital (n + ℓ = 6 + 2 = 8). The rule then predicts the electron configuration [Rn]5f47s2 where [Rn] denotes the configuration of the preceding noble gas radon. However the measured electron configuration of the uranium atom is [Rn]5f36d17s2.

A special exception is lawrencium 103Lr, where the 6d electron predicted by the Madelung rule is replaced by a 7p electron: the rule predicts [Rn]5f146d17s2, but the measured configuration is [Rn]5f147s27p1.

Atom 103Lr
Core electrons [Rn]
Madelung Rule 5f146d17s2
Experiment 5f147s27p1

History

The aufbau principle in the new quantum theory

Sommerfeld ellipses
In the old quantum theory, orbits with low angular momentum (s- and p-orbitals) get closer to the nucleus.

The principle takes its name from the German, Aufbauprinzip, "building-up principle", rather than being named for a scientist. In fact, it was formulated by Niels Bohr and Wolfgang Pauli in the early 1920s, and states that:

The orbitals of lower energy are filled in first with the electrons and only then the orbitals of high energy are filled.

This was an early application of quantum mechanics to the properties of electrons, and explained chemical properties in physical terms. Each added electron is subject to the electric field created by the positive charge of the atomic nucleus and the negative charge of other electrons that are bound to the nucleus. Although in hydrogen there is no energy difference between orbitals with the same principal quantum number n, this is not true for the outer electrons of other atoms.

In the old quantum theory prior to quantum mechanics, electrons were supposed to occupy classical elliptical orbits. The orbits with the highest angular momentum are 'circular orbits' outside the inner electrons, but orbits with low angular momentum (s- and p-orbitals) have high orbital eccentricity, so that they get closer to the nucleus and feel on average a less strongly screened nuclear charge.

The n + ℓ energy ordering rule

A periodic table in which each row corresponds to one value of n + ℓ was suggested by Charles Janet in 1927. In 1936, the German physicist Erwin Madelung proposed his empirical rules for the order of filling atomic subshells, based on knowledge of atomic ground states determined by the analysis of atomic spectra, and most English-language sources therefore refer to the Madelung rule. Madelung may have been aware of this pattern as early as 1926.[8] In 1962 the Russian agricultural chemist V.M. Klechkowski proposed the first theoretical explanation for the importance of the sum n + ℓ, based on the statistical Thomas–Fermi model of the atom.[9] Many French- and Russian-language sources therefore refer to the Klechkowski rule.

In recent years it has been noted that the order of filling orbitals in neutral atoms does not always correspond to the order of adding or removing electrons for a given atom. For example, in the fourth row of the periodic table the Madelung rule indicates that the 4s orbital is occupied before the 3d. The neutral atom ground state configurations are therefore K = (Ar)4s, Ca = (Ar)4s2, Sc = (Ar)4s23d, etc. However if a scandium atom is ionized by removing electrons (only), the configurations are Sc = (Ar)4s23d, Sc+ = (Ar)4s3d, Sc2+ = (Ar)3d. The orbital energies and their order depend on the nuclear charge; 4s is lower than 3d as per the Madelung rule in K with 19 protons, but 3d is lower in Sc2+ with 21 protons. The Madelung rule should only be used for neutral atoms.

In addition to there being ample experimental evidence to support this view, it makes the explanation of the order of ionization of electrons in this and other transition metals far more intelligible, given that 4s electrons are invariably preferentially ionized.[10]

See also

References

  1. ^ Cottingham, W. N.; Greenwood, D. A. (1986). "Chapter 5: Ground state properties of nuclei: the shell model". An introduction to nuclear physics. Cambridge University Press. ISBN 0-521-31960-9.
  2. ^ "Electron Configuration". WyzAnt.
  3. ^ Miessler, Gary L.; Tarr, Donald A. (1998). Inorganic Chemistry (2nd ed.). Prentice Hall. p. 38. ISBN 0-13-841891-8.
  4. ^ Jolly, William L. (1984). Modern Inorganic Chemistry (1st ed.). McGraw-Hill. p. 11. ISBN 0-07-032760-2.
  5. ^ Weinhold, Frank; Landis, Clark R. (2005). Valency and bonding: A Natural Bond Orbital Donor-Acceptor Perspective. Cambridge: Cambridge University Press. pp. 715–716. ISBN 0-521-83128-8.
  6. ^ Scerri, Eric R. (1998). "How Good is the Quantum Mechanical Explanation of the Periodic System?" (PDF). J. Chem. Educ. 75 (11): 1384–85. Bibcode:1998JChEd..75.1384S. doi:10.1021/ed075p1384.
  7. ^ Meek, Terry L.; Allen, Leland C. (2002). "Configuration irregularities: deviations from the Madelung rule and inversion of orbital energy levels". Chem. Phys. Lett. 362 (5–6): 362–64. Bibcode:2002CPL...362..362M. doi:10.1016/S0009-2614(02)00919-3.
  8. ^ Goudsmit, S. A.; Richards, Paul I. (1964). "The Order of Electron Shells in Ionized Atoms" (PDF). Proc. Natl. Acad. Sci. 51 (4): 664–671 (with correction on p&nbsp, 906). Bibcode:1964PNAS...51..664G. doi:10.1073/pnas.51.4.664. PMC 300183.
  9. ^ Wong, D. Pan (1979). "Theoretical justification of Madelung's rule". J. Chem. Educ. 56 (11): 714–718. Bibcode:1979JChEd..56..714W. doi:10.1021/ed056p714.
  10. ^ Scerri, Eric (7 November 2013). "The Trouble With the Aufbau Principle". Education in Chemistry. Vol. 50 no. 6. Royal Society of Chemistry. pp. 24–26.

Further reading

External links

D electron count

The d electron count is a chemistry formalism used to describe the electron configuration of the valence electrons of a transition metal center in a coordination complex. The d electron count is an effective way to understand the geometry and reactivity of transition metal complexes. The formalism has been incorporated into the two major models used to describe coordination complexes; crystal field theory and ligand field theory, which is a more advanced version based on molecular orbital theory.

Darmstadtium

Darmstadtium is a synthetic chemical element with the symbol Ds and atomic number 110. It is an extremely radioactive synthetic element. The most stable known isotope, darmstadtium-281, has a half-life of approximately 12.7 seconds. Darmstadtium was first created in 1994 by the GSI Helmholtz Centre for Heavy Ion Research near the city of Darmstadt, Germany, after which it was named.

In the periodic table, it is a d-block transactinide element. It is a member of the 7th period and is placed in the group 10 elements, although no chemical experiments have yet been carried out to confirm that it behaves as the heavier homologue to platinum in group 10 as the eighth member of the 6d series of transition metals. Darmstadtium is calculated to have similar properties to its lighter homologues, nickel, palladium, and platinum.

Diatomic carbon

Diatomic carbon (systematically named dicarbon and 1λ2,2λ2-ethene, is a green, gaseous inorganic chemical with the chemical formula C=C (also written [C2] or C2). It is kinetically unstable at ambient temperature and pressure, being removed through autopolymerisation. It occurs in carbon vapor, for example in electric arcs; in comets, stellar atmospheres and the interstellar medium; and in blue hydrocarbon flames.

Diatomic carbon is the second simplest form of carbon after atomic carbon, and is an intermediate participator in the genesis of fullerenes.

Dividing line between metals and nonmetals

The dividing line between metals and nonmetals can be found, in varying configurations, on some representations of the periodic table of the elements (see mini-example, right). Elements to the lower left of the line generally display increasing metallic behaviour; elements to the upper right display increasing nonmetallic behaviour. When presented as a regular stair-step, elements with the highest critical temperature for their groups (Li, Be, Al, Ge, Sb, Po) lie just below the line.

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 atom is 1s2 2s2 2p6, using the notation explained below.

Electronic configurations describe each electron as moving independently in an orbital, in an average field created by all other orbitals. Mathematically, configurations are described by Slater determinants or configuration state functions.

According to the laws of quantum mechanics, for systems with only one electron, a level of energy is associated with each electron configuration and in certain conditions, electrons are able to move from one configuration to another by the emission or absorption of a quantum of energy, in the form of a photon.

Knowledge of the electron configuration of different atoms is useful in understanding the structure of the periodic table of elements. This is also useful for describing the chemical bonds that hold atoms together. In bulk materials, this same idea helps explain the peculiar properties of lasers and semiconductors.

Electron configurations of the elements (data page)

This page shows the electron configurations of the neutral gaseous atoms in their ground states. For each atom the subshells are given first in concise form, then with all subshells written out, followed by the number of electrons per shell. Electron configurations of elements beyond hassium (element 108) are predicted.

As an approximate rule, electron configurations are given by the Aufbau principle and the Madelung rule. However there are numerous exceptions; for example the lightest exception is chromium, which would be predicted to have the configuration 1s2 2s2 2p6 3s2 3p6 3d4 4s2, written as [Ar] 3d4 4s2, but whose actual configuration given in the table below is [Ar] 3d5 4s1.

Electron shell

In chemistry and atomic physics, an electron shell, or a principal energy level, may be thought of as an orbit followed by electrons around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), and so on farther and farther from the nucleus. The shells correspond with the principal quantum numbers (n = 1, 2, 3, 4 ...) or are labeled alphabetically with letters used in the X-ray notation (K, L, M, …).

Each shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the nth shell can in principle hold up to 2(n2) electrons. Since electrons are electrically attracted to the nucleus, an atom's electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons. However, this is not a strict requirement: atoms may have two or even three incomplete outer shells. (See Madelung rule for more details.) For an explanation of why electrons exist in these shells see electron configuration.The electrons in the outermost occupied shell (or shells) determine the chemical properties of the atom; it is called the valence shell.

Each shell consists of one or more subshells, and each subshell consists of one or more atomic orbitals.

Energy level

A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy levels. The term is commonly used for the energy levels of electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules. The energy spectrum of a system with such discrete energy levels is said to be quantized.

In chemistry and atomic physics, an electron shell, or a principal energy level, may be thought of as an orbit followed by electrons around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), and so on farther and farther from the nucleus. The shells correspond with the principal quantum numbers (n = 1, 2, 3, 4 ...) or are labeled alphabetically with letters used in the X-ray notation (K, L, M, …).

Each shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the nth shell can in principle hold up to 2(n2) electrons. Since electrons are electrically attracted to the nucleus, an atom's electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons. However, this is not a strict requirement: atoms may have two or even three incomplete outer shells. (See Madelung rule for more details.) For an explanation of why electrons exist in these shells see electron configuration.If the potential energy is set to zero at infinite distance from the atomic nucleus or molecule, the usual convention, then bound electron states have negative potential energy.

If an atom, ion, or molecule is at the lowest possible energy level, it and its electrons are said to be in the ground state. If it is at a higher energy level, it is said to be excited, or any electrons that have higher energy than the ground state are excited. If more than one quantum mechanical state is at the same energy, the energy levels are "degenerate". They are then called degenerate energy levels.

Group 10 element

Group 10, numbered by current IUPAC style, is the group of chemical elements in the periodic table that consists of nickel (Ni), palladium (Pd), platinum (Pt), and perhaps also the chemically uncharacterized darmstadtium (Ds). All are d-block transition metals. All known isotopes of darmstadtium are radioactive with short half-lives, and are not known to occur in nature; only minute quantities have been synthesized in laboratories.

Like other groups, the members of this group show patterns in electron configuration, especially in the outermost shells, although for this group they are particularly weak, with palladium being an exceptional case. The relativistic stabilization of the 7s orbital is the explanation to the predicted electron configuration of darmstadtium, which, unusually for this group, conforms to that predicted by the Aufbau principle.

Group 3 element

Group 3 is a group of elements in the periodic table. This group, like other d-block groups, should contain four elements, but it is not agreed what elements belong in the group. Scandium (Sc) and yttrium (Y) are always included, but the other two spaces are usually occupied by lanthanum (La) and actinium (Ac), or by lutetium (Lu) and lawrencium (Lr); less frequently, it is considered the group should be expanded to 32 elements (with all the lanthanides and actinides included) or contracted to contain only scandium and yttrium. When the group is understood to contain all of the lanthanides, its trivial name is the rare-earth metals.

Three group 3 elements occur naturally: scandium, yttrium, and either lanthanum or lutetium. Lanthanum continues the trend started by two lighter members in general chemical behavior, while lutetium behaves more similarly to yttrium. While the choice of lutetium would be in accordance with the trend for period 6 transition metals to behave more similarly to their upper periodic table neighbors, the choice of lanthanum is in accordance with the trends in the s-block, which the group 3 elements are chemically more similar to. They all are silvery-white metals under standard conditions. The fourth element, either actinium or lawrencium, has only radioactive isotopes. Actinium, which occurs only in trace amounts, continues the trend in chemical behavior for metals that form tripositive ions with a noble gas configuration; synthetic lawrencium is calculated and partially shown to be more similar to lutetium and yttrium. So far, no experiments have been conducted to synthesize any element that could be the next group 3 element. Unbiunium (Ubu), which could be considered a group 3 element if preceded by lanthanum and actinium, might be synthesized in the near future, it being only three spaces away from the current heaviest element known, oganesson.

Hund's rule of maximum multiplicity

Hund's rule of maximum multiplicity is a rule based on observation of atomic spectra, which is used to predict the ground state of an atom or molecule with one or more open electronic shells. The rule states that for a given electron configuration, the lowest energy term is the one with the greatest value of spin multiplicity. This implies that if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pairs. The rule, discovered by Friedrich Hund in 1925, is of important use in atomic chemistry, spectroscopy, and quantum chemistry, and is often abbreviated to Hund's rule, ignoring Hund's other two rules.

Light metal

A light metal is any metal of relatively low density. More specific definitions have been proposed; none have obtained widespread acceptance. Magnesium, aluminium and titanium are light metals of significant commercial importance. Their densities of 1.7, 2.7 and 4.5 g/cm3 range from 19 to 56% of the densities of the older structural metals, iron (7.9) and copper (8.9).

List of people whose names are used in chemical element names

Below is the list of people whose names are used in chemical element names. Of the 118 chemical elements, 19 are connected with the names of 20 people. 15 elements were named to honor 16 scientists. Four other elements have indirect connection to the names of non-scientists. Only gadolinium and samarium occur in nature; the rest are synthetic.

List of places used in the names of chemical elements

40 of the 118 chemical elements have names associated with, or specifically named for, places around the world or among astronomical objects. 32 of these have names tied to the Earth and the other 8 have names connected to bodies in the Solar System. The first tables below list the terrestrial locations (excluding the entire Earth itself, taken as a whole) and the last table lists astronomical objects which the chemical elements are named after.

Spin states (d electrons)

Spin states when describing transition metal coordination complexes refers to the potential spin configurations of the central metal's d electrons. In many these spin states vary between high-spin and low-spin configurations. These configurations can be understood through the two major models used to describe coordination complexes; crystal field theory and ligand field theory, which is a more advanced version based on molecular orbital theory.

Systematic element name

A systematic element name is the temporary name assigned to a newly synthesized or not yet synthesized chemical element. A systematic symbol is also derived from this name. In chemistry, a transuranic element receives a permanent name and symbol only after its synthesis has been confirmed. In some cases, such as the Transfermium Wars, controversies over the formal name and symbol have been protracted and highly political. In order to discuss such elements without ambiguity, the International Union of Pure and Applied Chemistry (IUPAC) uses a set of rules to assign a temporary systematic name and symbol to each such element. This approach to naming originated in the successful development of regular rules for the naming of organic compounds.

Transition metal

In chemistry, the term transition metal (or transition element) has three possible meanings:

The IUPAC definition defines a transition metal as "an element whose atom has a partially filled d sub-shell, or which can give rise to cations with an incomplete d sub-shell".

Many scientists describe a "transition metal" as any element in the d-block of the periodic table, which includes groups 3 to 12 on the periodic table. In actual practice, the f-block lanthanide and actinide series are also considered transition metals and are called "inner transition metals".

Cotton and Wilkinson expand the brief IUPAC definition (see above) by specifying which elements are included. As well as the elements of groups 4 to 11, they add scandium and yttrium in group 3, which have a partially filled d subshell in the metallic state. Lanthanum and actinium in group 3 are, however, classified as lanthanides and actinides respectively.English chemist Charles Bury (1890–1968) first used the word transition in this context in 1921, when he referred to a transition series of elements during the change of an inner layer of electrons (for example n = 3 in the 4th row of the periodic table) from a stable group of 8 to one of 18, or from 18 to 32. These elements are now known as the d-block.

Unbiquadium

Unbiquadium, also known as element 124 or eka-uranium, is the hypothetical chemical element with atomic number 124 and placeholder symbol Ubq. Unbiquadium and Ubq are the temporary IUPAC name and symbol, respectively, until the element is discovered, confirmed, and a permanent name is decided upon. In the periodic table, unbiquadium is expected to be a g-block superactinide and the sixth element in the 8th period. Unbiquadium has attracted attention, as it may lie within the island of stability, leading to longer half-lives, especially for 308Ubq which is predicted to have a magic number of neutrons (184).

Despite several searches, unbiquadium has not been synthesized, nor have any naturally occurring isotopes been found to exist. It is believed that the synthesis of unbiquadium will be far more challenging than that of lighter undiscovered elements, and nuclear instability may pose further difficulties in identifying unbiquadium, unless the island of stability has a stronger stabilizing effect than predicted in this region.

As a member of the superactinide series, unbiquadium is expected to bear some resemblance to its possible lighter congener uranium. The valence electrons of unbiquadium are expected to participate in chemical reactions fairly easily, though relativistic effects may significantly influence some of its properties; for example, the electron configuration has been calculated to differ considerably from the one predicted by the Aufbau principle.

Wiswesser rule

The Wiswesser rule gives a simple method to determine the energetic sequence of the atomic subshells , where n is the principal quantum number and is the azimuthal quantum number. The energetic sequence of the subshells characterized by the quantum numbers is the sequence that leads to a monotonically increasing row of function values for the Wiswesser function. The rule is named after William Wiswesser.

For example: if and , this corresponds to a 2p-orbital.

If the results of this function for each shell and subshell are ordered, the resulting sequence is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p...

To illustrate this, the corresponding values of each of these shells can be found in the table below:

We can now clearly see that the aufbau principle and Wiswesser's rule come to the same order of filling electron shells.

Quantum numbers
Periodic table
Principles

This page is based on a Wikipedia article written by authors (here).
Text is available under the CC BY-SA 3.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.