# Atomic orbital

Atomic orbital or is an area of ​​space where there is a high probability (greater than 90%) of finding the electron.

Summary

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• 1 Origin
• 1 Quantum numbers
• 2 Orbitals
• 1 Orbitals according to the value of quantum numbers
• 3 Types of orbitals
• 1 Orbital s
• 2 Orbital p
• 3 Orbital d
• 4 Orbital f
• 5 Source

Origin

This involves considering the electron as a diffuse cloud of charge around the nucleus with the highest density in areas where the probability of such an electron being found is greater. For the Schrödinger equation to have physical meaning it is necessary to impose restrictions on it that are known as quantum numbers, which are symbolized in the same way as those obtained in Bohr’s atomic model:

Quantum numbers

• n: main quantum number
• l: quantum number of the orbital angular momentum
• m: magnetic quantum number
• s: quantum number of the electronic spin.

These quantum numbers can only take certain allowed values:

Allowed values

• for n: integers 1, 2, 3 ,.
• for l: integers from 0 to (n-1)
• for m: all integers between + l and -l including 0
• for s: only fractional numbers -1/2 and +1/2

The values ​​of the quantum number n indicate the size of the orbital, that is, its proximity to the nucleus. The values ​​of the quantum number l define the type of orbital:

• If l = 0 the orbital is of type s • If l = 1 the orbitals are of type p • If l = 2 the orbitals are of type d • If l = 3 the orbitals are of type f

The letters s, p, d, f identifying the types of orbitals come from the names received by the different groups of spectral lines related to each of the orbitals:

• sharp: sharp but low intensity lines • main: strong lines • diffuse: diffuse lines • fundamental: frequent lines in many spectra

Other types of orbitals such as g, h, … are possible, but the elements that we know, in their ground state, do not have electrons that meet the quantum conditions necessary for these other types of orbitals to occur. The quantum number values ​​m refer to the spatial orientation of the orbital. The fourth quantum number, s, that defines an electron in an atom refers to its angular momentum of rotation. The set of the four quantum numbers define an electron, since two electrons with the same four quantum numbers cannot exist in the same atom, so once the size, type and orientation of an orbital with the first three numbers have been defined quantum, that is, the values ​​of n, l and m,

Orbitals

An atomic orbital is a mathematical function that describes the wave-like behavior of both an electron and a pair of them in an atom. As mathematical functions, they can be used in linear combinations (that is, they can be added and subtracted). This function can be used to calculate the probability of finding the electron in any area within the atomic nucleus. These functions can serve as three-dimensional graphs of the most probable location of the electron. The term can directly refer to the physical region defined by that function. Specifically, atomic orbitals are the possible quantum states of an individual electron in the group of atoms around a single atom.

Despite the obvious analogy of planets around a sun, electrons cannot be described as solid particles and furthermore rarely do atomic orbitals resemble the elliptical paths of the planets. A more accurate comparison may be that of an extensive but oddly shaped atmosphere (the electron), distributed around a relative small planet (the atomic nucleus). Atomic orbitals accurately describe the shape of this atmosphere only when a single electron is present in the atom. When more electrons are added, they tend to fill a volume in space near the nucleus so that the resulting group (sometimes called the “electronic cloud”) changes to a more or less spherical shape, describing the probability zone where the electrons can be found.

The simplest atomic orbitals are those in an atom with one electron, as in the hydrogen atom. An atom of any other element ionized to an electron is very similar to hydrogen , and the orbits take the same shape (hence the name hydrogen atoms / orbitals).

For atoms with two or more electrons, the relevant equations can only be solved with iterative methods. However, the orbitals of multi-electron atoms are qualitatively similar to those of hydrogen, and in the simplest models, they are assumed to be the same. For more rigorous and precise analyzes, numerical approximations should be used.

An atomic orbital (hydrogen) is identified by values ​​of three quantum numbers: n, l, and ml. The restriction rules of the values ​​acquired by the quantum numbers and their energies explain the electronic configuration of the atoms in the periodic table.

n can take any positive integer value, although the greater the number it represents the greater the energy and the greater the instability. l can take values ​​from 0 to n-1, this quantum number determines the shape of the orbital: l = 0 is represented as “s” and they are spherical orbitals, l = 1 is represented by “p” s are orbitals with two lobes, l = 2 is represented by “d”, l = 3 is represented by “f” and from l = 4, “g” already follows alphabetical order of nomenclature. The quantum number ml goes from -l to + l going through 0 and in whole units. Furthermore, there is the quantum number ms, which for electrons can be 1/2 or -1/2, which determines their spin state. There cannot be two electrons with all four quantum numbers equal.

The quantum number n first appeared in Bohr’s atomic model. It determines, among other things, the distance from the electron to the nucleus; all electrons with the same value of n are at approximately the same distance. Modern quantum mechanics confirms that these orbitals are closely related. For this reason, orbitals with the same value of n are said to form a “shell”. Orbitals with the same value of n and the same value of l are even more closely linked, and are said to form a “sublayer”.