Aufbau principle

The aufbau principle, from the German Aufbauprinzip, “to build” (also called the building-up principle or the aufbau rule) 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, and so on. The aufbau principle, from the German Aufbauprinzip, “to build” (also called the building-up principle or the aufbau rule) 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, and so on. 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: 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 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. Other authors write the orbitals always in order of increasing n, such as Ti (Z = 22) 1s2 2s2 2p6 3s2 3p6 3d2 4s2. This can be called 'leaving order', since if the atom is ionized, electrons leave approximately 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. Orbitals with a lower n + ℓ value are filled before those with higher n + ℓ values. In the case of equal n + ℓ values, the orbital with a lower n value is filled first. The Madelung energy ordering rule applies only to neutral atoms in their ground state. There are ten elements among the transition metals and ten elements among the lanthanides and actinides for which the Madelung rule predicts an electron configuration that differs from that determined experimentally. Metaphorically speaking, these exceptions can be viewed as turbulence along a flight path; once passed the flight path returns to normal. One inorganic chemistry textbook describes the Madelung rule as essentially an approximate empirical rule although with some theoretical justification, based on the Thomas-Fermi model of the atom as a many-electron quantum-mechanical system.