The Concept of Quantum Numbers

Quantum numbers in quantum mechanics and chemistry are used to describe the dynamics of conserved quantities in quantum systems. Essentially, quantum numbers are eigenvalues of operators whose Hamiltonian amounts divide with precision, and which can be determined simultaneously with the system’s energy and eigenspaces. All of a quantum system’s quantum numbers combined describe the system’s actual state in a manner that can, in theory, be measured together.

Quantum physics is characterized by the quantification of numerous observable quantities of interest. Quantum numbers, in particular, represent discrete sets of integers or half-integers as values, although in some cases they approach infinity. Quantum mechanics differs from classical mechanics, in which the properties of the system, such as mass, charge, and momentum, are constantly changing.

What are Quantum Numbers and How Do They Work?

In quantum mechanics, quantum numbers represent the values of the preserved quantities in a quantum system. The electronic quantum numbers (the quantum numbers that describe electrons) can be described as numerical values that yield the Schrodinger wave equation solutions for hydrogen atoms. A complete description of all the characteristics of an atom’s electrons can be expressed using these four quantum numbers:

1. Quantum number N is the principal number.
2. An orbital angular momentum quantum number (also known as an azimuthal quantum number) is indicated by the letter L.
3. A magnetic quantum number is represented by ML.
4. Quantum number of electron spin is called Ms.

Principal Quantum Number 

Principal quantum numbers are represented by the symbol ‘n’. Primary electron shells are determined by these numbers. A greater direct quantum number corresponds to a larger distance between the nucleus and the electrons (which is a relevant indication of larger atomic size), since it describes the most probable distance between the nucleus and the electrons.

Any positive integer with a value greater than one or equal to one can be used as the principal quantum number’s value. Atoms that have n=1 have their innermost electron shell, which corresponds to the lowest energy states of electrons (or their ground state).

Therefore, n cannot be negative or zero when applied to the principal quantum number, since an atom cannot have a negative or zero value for its top shell.

The energy infuses electrons with higher energy levels (excited state), which increases the value of the number n. Conversely, when electrons lose power, they return to lower energy levels, which decreases n.

Absorption is an increase in n for an electron, which highlights the photons or energy absorbed by the electron. It is the release of electron energy that causes the value of n for an electron to drop.

Azimuthal Quantum Number

Azimuthal (orbital angular momentum) quantum number describes the form of an orbital. The symbol ‘l’ indicates the number of angular nodes in the orbital, where its value equals the number of angular nodes within the orbital.

There is no single form of an azimuthal quantum number, but different forms are possible for s, p, d, and f subshells. The azimuthal quantum number varies between 0 and 1. This value is determined by the primary quantum number (and thereby limited by it). (n-1).

In the case of n = 3, the azimuthal quantum number can be 0, 1, or 2. In cases where l=0, the resulting subshell is an ‘s’ subshell. ‘P’ and ‘D’ subshells are subsequently formed when l=1 and l=2. There are three subshells that can be used when n=3. These are 3s, 3p, and 3d.

A further example is when the value of n is 5, l can take the values 0, 1, 2, 3, and 4. A three-node atom has three angular nodes if l = 3.

Quantum Number for Magnetism

In each subshell, the number of orbitals and the orientation of those orbitals is determined by the magnetic quantum number. It is represented by the symbol ML. The angular momentum of the orbital is represented by this value along that specific axis.

The magnetic quantum number is determined by the azimuthal quantum number (orbital angular momentum). An exact value of ml for a particular value of l falls within the range of -l to +l. Consequently, the weight of n indirectly affects it.

Quantum Number of Electron Spin

The electron spin quantum number is independent of the values of n, l, and ml. This number indicates the direction an electron is spinning. Accordingly, the symbol ms represents the value of this number.

The value of ms represents the spin direction of the electron. There are two potential values of the electron spin quantum number.

Conclusion 

Quantum numbers are frequently used to represent electron energy levels in atoms, but they can also refer to concepts such as angular momentum and spin. Particles and those particles’ interactions with other particles are determined by their internal quantum numbers, which are a fundamental family. Quantum systems can have one or more quantum numbers, so listing all possible quantum numbers can be challenging.