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Aufbau principle
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Aufbau principle
In atomic physics and quantum chemistry, the Aufbau principle (/ˈaʊfbaʊ/, from German: Aufbauprinzip, lit. 'building-up principle'), also called the Aufbau rule, states that in the ground state of an atom or ion, electrons first fill subshells of the lowest available energy, then fill subshells of higher energy. For example, the 1s subshell 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 3p6 4s2 3d10 for the zinc atom, meaning that the 1s subshell has 2 electrons, the 2s subshell has 2 electrons, the 2p subshell has 6 electrons, and so on.
The configuration is often abbreviated by writing only the valence electrons explicitly, while the core electrons are replaced by the symbol for the last previous noble gas in the periodic table, placed in square brackets. For zinc, the last previous noble gas is argon, so the configuration is abbreviated to [Ar] 4s2 3d10, where [Ar] signifies the core electrons whose configuration in zinc is identical to that of argon.
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 and with the same spin before any are occupied doubly. If double occupation does occur, the Pauli exclusion principle requires that electrons that occupy the same orbital must have different spins (+1⁄2 and −1⁄2).
Passing from one element to another of the 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 is equal to 2(2l + 1), where the azimuthal quantum number l is equal to 0, 1, 2, and 3 for s, p, d, and f subshells, so that the maximum numbers of electrons are 2, 6, 10, and 14 respectively. In the ground state, the electronic configuration can be built up by placing electrons in the lowest available subshell until the total number of electrons added is equal to the atomic number. Thus subshells are filled in the order of increasing energy, using two general rules to help predict electronic configurations:
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.
In neutral atoms, the approximate order in which subshells are filled is given by the n + l rule, also known as the:
Here n represents the principal quantum number and l the azimuthal quantum number; the values l = 0, 1, 2, 3 correspond to the s, p, d, and f subshells, respectively. Subshells with a lower n + l value are filled before those with higher n + l values. In the many cases of equal n + l values, the subshell with a lower n value is filled first. 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, 5g, ... For example, thallium (Z = 81) has the ground-state configuration 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p1 or in condensed form, [Xe] 6s2 4f14 5d10 6p1.
Other authors write the subshells outside of the noble gas core in order of increasing n, or if equal, increasing n + l, such as Tl (Z = 81) [Xe]4f14 5d10 6s2 6p1. They do so to emphasize that if this atom is ionized, electrons leave approximately in the order 6p, 6s, 5d, 4f, etc. On a related note, writing configurations in this way emphasizes the outermost electrons and their involvement in chemical bonding.
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Aufbau principle
In atomic physics and quantum chemistry, the Aufbau principle (/ˈaʊfbaʊ/, from German: Aufbauprinzip, lit. 'building-up principle'), also called the Aufbau rule, states that in the ground state of an atom or ion, electrons first fill subshells of the lowest available energy, then fill subshells of higher energy. For example, the 1s subshell 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 3p6 4s2 3d10 for the zinc atom, meaning that the 1s subshell has 2 electrons, the 2s subshell has 2 electrons, the 2p subshell has 6 electrons, and so on.
The configuration is often abbreviated by writing only the valence electrons explicitly, while the core electrons are replaced by the symbol for the last previous noble gas in the periodic table, placed in square brackets. For zinc, the last previous noble gas is argon, so the configuration is abbreviated to [Ar] 4s2 3d10, where [Ar] signifies the core electrons whose configuration in zinc is identical to that of argon.
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 and with the same spin before any are occupied doubly. If double occupation does occur, the Pauli exclusion principle requires that electrons that occupy the same orbital must have different spins (+1⁄2 and −1⁄2).
Passing from one element to another of the 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 is equal to 2(2l + 1), where the azimuthal quantum number l is equal to 0, 1, 2, and 3 for s, p, d, and f subshells, so that the maximum numbers of electrons are 2, 6, 10, and 14 respectively. In the ground state, the electronic configuration can be built up by placing electrons in the lowest available subshell until the total number of electrons added is equal to the atomic number. Thus subshells are filled in the order of increasing energy, using two general rules to help predict electronic configurations:
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.
In neutral atoms, the approximate order in which subshells are filled is given by the n + l rule, also known as the:
Here n represents the principal quantum number and l the azimuthal quantum number; the values l = 0, 1, 2, 3 correspond to the s, p, d, and f subshells, respectively. Subshells with a lower n + l value are filled before those with higher n + l values. In the many cases of equal n + l values, the subshell with a lower n value is filled first. 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, 5g, ... For example, thallium (Z = 81) has the ground-state configuration 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p1 or in condensed form, [Xe] 6s2 4f14 5d10 6p1.
Other authors write the subshells outside of the noble gas core in order of increasing n, or if equal, increasing n + l, such as Tl (Z = 81) [Xe]4f14 5d10 6s2 6p1. They do so to emphasize that if this atom is ionized, electrons leave approximately in the order 6p, 6s, 5d, 4f, etc. On a related note, writing configurations in this way emphasizes the outermost electrons and their involvement in chemical bonding.
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