What Is an Atomic Orbital?

Atomic orbits, also called orbital states , are mathematical functions that describe the wavelike behavior of electrons in atoms. This wave function can be used to calculate the probability of finding electrons in an atom in a specific space outside the nucleus, and indicate the possible positions of the electrons in three-dimensional space. "Orbit" refers to a region where electrons have a higher probability of appearing in the outer space of the nucleus under the definition of a wave function. Specifically, atomic orbits are the possible quantum states of individual electrons among the many electrons (electron clouds) that surround an atom, and are described by orbital wave functions.

Atomic orbital theorem

The motion of electrons in atomic orbits follows three basic theorems: the principle of minimum energy, Pauli's incompatible principle, and Hund's rule.

Atomic orbit

The principle of the lowest energy means that when the electrons outside the nucleus are in motion, they always occupy the orbit with lower energy first, so that the entire system is in the lowest energy state.

Physicist Pauli put forward on the basis of summarizing many facts: it is impossible for two identical fermions to have the same quantum physical state at the same time. The Pauli exclusion principle is applied to the arrangement of electrons and can be expressed as: up to two electrons with opposite spins can be accommodated in the same orbit. This principle has three inferences:

If two electrons are in the same orbit, their spin directions must be different;

If two electrons have the same spin, they must not be in the same orbit;

Each orbit can accommodate up to two electrons.

Atomic orbital Hund rule

Hundt proposed Hund's rule on the basis of summarizing a large amount of spectrum and ionization potential data: when electrons are arranged on degenerate orbits, they will occupy different orbits as much as possible, and the spins are parallel ^[4] . For the same electron sublayer, when the electron arrangement is

Full (s ² , p ⁶ , d ¹⁰ , f ¹⁴ )

Half full (s ¹ , p ³ , d ⁵ , f ⁷ )

All empty (s ⁰ , p ⁰ , d ⁰ , f ⁰ )

Is relatively stable.

Atomic orbital electron arrangement

Initially, people only used the schematic diagram of the electronic structure to represent the microstructure of the atom, but the schematic diagram of the electronic structure can only show the electron layer of the atom, but not the energy level and orbit, and the electronic arrangement was born ^[5] .

The electronic arrangement is expressed as follows: the number in front of the energy level symbol indicates the electron layer in which the energy level is located, and the index after the energy level symbol indicates the number of electrons in the energy level. The order of the order and the three rules of "the principle of minimum energy", "Pawley's incompatible principle" and "Hunde's rule". In addition, although the electron first enters the 4s orbit and then enters the 3d orbit (the order of energy level interleaving), it still proceeds in the order of 1s 2s, 2p 3s, 3p, 3d 4s.

Example

H: 1s ¹

F: 1s ² 2s ² , 2p ⁵

S: 1s ² 2s ² , 2p ⁶ 3s ² , 3p ⁴

Cr: 1s ² 2s ² , 2p ⁶ 3s ² , 3p ⁶ , 3d ⁵ 4s ¹ It is semi-full, which reflects Hund's rule).

Simplified electronic layout

For writing convenience, the electronic arrangement is usually simplified, and the already filled electronic layer is replaced with a rare gas structure.

Example

Cr: 1s ² 2s ² , 2p ⁶ 3s ² , 3p ⁶ , 3d ⁵ 4s ¹

Simplified: Cr: [Ar] 3d ⁵ 4s ¹ (because Ar: 1s ² 22s ² , 2p ⁶ 63s ² , 3p ⁶ )

The remaining part of the electron arrangement after simplification is valence electrons, which will participate in chemical reactions and are marked in the periodic table.