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The different theories gave rise to the four quantum numbers. These numbers are used to explain the characteristics of the electrons in an atom. Quantum numbers have the following values and properties:
The principal quantum number
It is symbolized as ” n ” and indicates the energy levels possessed by an atom. That is, the energy level where an electron moves. It also allows us to calculate the approximate distance between the nucleus of the atom and the electron. Likewise, it allows us to recognize the size of the orbital where the electron is located. The value of this quantum number is an integer from 1 onwards. So far only atoms with 8 energy levels at most are known.
The secondary or azimuthal quantum number
It is represented by the letter « l » and indicates the specific orbital where an electron is located. It also indicates the energy sublevel of an electron. The value of “l” can be: 0, 1, 2,… up to -1. Orbitals, in turn, have different shapes. They can be classified into:
- “s” if l=0;
- “p” if l=1;
- “d” if l=2; and
- “f” if l = 3.
The magnetic quantum number
« m » is the magnetic quantum number , also called angular momentum, and marks the orientation of the orbitals in space. It also indicates the number of orbitals for each sublevel. It can have a negative quantum number value “l” (-l), (0) or a positive secondary quantum number (+l).
The spin quantum number
- The spin quantum number (or spin) is symbolized by the letter “s”. This number indicates the direction of rotation of the electrons on an imaginary axis. It can take the fractional values: 1/2 and -1/2.
Other characteristics of quantum numbers
In addition to the values mentioned, quantum numbers also have other special characteristics:
- They indicate the position of the energy of an electron.
- According to the Pauli Principle, no electron in the same atom can have the same quantum numbers.
- According to a Schrödinger theory, depending on the values of the quantum numbers, different solutions of wave equations are obtained. These results will allow us to know the places that have a higher probability of having an electron.
- The electron spin “s” is a characteristic property of electrons. This is because they have their own angular momentum, indicated by the quantum number.
- Each energy sublevel contains one or more orbitals. The number of these orbitals in each sublevel and their spatial orientation are determined by the magnetic quantum number.
- Although quantum numbers are used primarily to describe electrons, they can also describe the protons and neutrons in an atom.
Examples of quantum numbers
In order to analyze the electrons of an atom and apply quantum numbers, a hydrogen atom is taken as an example. That is, an atom similar to that of hydrogen (H) is used, which has a single nucleus and a single electron. This type of atoms has values for the quantum numbers: “n”, “l” and “m”. On the other hand, in polyelectronic or several electron atoms, the quantum number “s” is also added.
Another example is the carbon atom (C), where the electrons are in the 2p orbital. The four quantum numbers used to describe the electrons in this atom are: n = 2; l = 1; m = 1, 0 or -1; ys = 1/2.
Bibliography
- Lahera Claramonte, J. From atomic theory to quantum physics: Bohr. 2010 (2nd Edition). Spain. Nivola Editions.
- Wurtz, A. The Atomic Theory . 2018. Spain. The Forgotten Books.
- Gillespie, GT Introduction to quantum mechanics. 2021 (1st Edition). Spain. reverse.
