Quantum Numbers

A quantum number is any of several integral or half-integral numbers that identify the state of a physical system, such as an atom, a nucleus, or a subatomic particle. Quantum numbers are discrete (quantised) and conserved properties that include energy, momentum, charge, baryon number, and lepton number.

For electrons bonded in atoms, for example, the fundamental quantum number indicates the energy state and the possibility of finding electrons at various distances from the nucleus. The larger the main quantum number, which has integral values beginning with one, the higher the energy and the farthest the electron is projected from the nucleus. The basic quantum number and three others can be used to identify each electron in an atom. A distinct set of quantum numbers defines the atomic nucleus.

In total, there are four quantum numbers:

• n – is the principal quantum number that depicts the level of energy.
• ℓ – azimuthal is the angular momentum of quantum number that narrates the amount of subshell.
• mℓ or m – is a magnetic quantum number that will describe the orbital of the subshell.
• ms or s – spin quantum number: describes the spin.

Values of Quantum Numbers

According to the Pauli exclusion principle, no two electrons in an atom may have the same set of quantum numbers. A half-integer or integer value is used to represent each quantum number.

• The principal quantum number(n), an integer, is the number of electron shells. One or more values are present (never 0 or negative).
• The angular momentum quantum number (s=0, p=1) represents the value of the electron’s orbital. (l) is a positive integer between n-1 and zero that is less than or equal to n-1. 

For example, if n = 3, the azimuthal quantum number can be 0, 1, or 2. The resulting subshell is n’s subshell, respectively. When n=3, the three subshells which could be used are 3s, 3p, and 3d. In another example, the possible values of l are 0, 1, 2, 3, and 4 when the value of n is 5. There are three angular nodes in the atom if l = 3. The acceptable subshells for numerous ‘n’ and ‘l’ combinations have been described above. Since this value of ‘l’ is always less than that of ‘n,’ the ‘2d’ orbital has been unable to exist.

• Understanding that you can only have one value for the first shell, say K, n = 1, i.e. l = 0; you can have two values for the second shell, say L, n = 2, i.e. l = 0 and 1; and three values for the third shell, say M, n = 3, i.e. l = 0, 1, and 2. 

• The magnetic quantum number is the orbital’s orientation, with integer values ranging from -l to l. As a consequence, m might be -1, 0, or 1 for the p orbital with l=1.For example, if n = 4 and l = 3 in an atom, the magnetic quantum number might be -3, -2, -1, 0, +1, +2, or +3.
• The spin quantum number is a half-integer variable that can be either -1/2 (spin down) or +1/2 (spin up) (called “spin up”).
• The Principal Quantum Number is the most important number in quantum mechanics (n)
• The primary electron shell is designated by the quantum number n. 
• Because n denotes the most likely distance between the nucleus and the electrons, the bigger the number n, the further the electron is from the nucleus, the larger the orbital, and the larger the atom. 
• Because n=1 indicates the first primary shell, n can be any positive number starting at 1. (the innermost shell). The ground state, or lowest energy state, is the first major shell.
• n cannot be 0 or any negative integer since there are no atoms with zero or a negative number of energy levels/principal shells. 
• When an electron is excited or accumulates energy, it might jump to the second main shell, where n=2. 
• Absorption is the process of an electron “absorbing” photons or energy. When electrons jump to lower primary shells, where n decreases by whole numbers, they can “emit” energy, a process known as emission. 
• The major quantum number rises as the electron’s energy increases; for example, n = 3 signifies the third primary shell, n = 4 the fourth, and so on.

Conclusion

The quantum numbers L, ML, S, MS, and J, MJ,, which define the magnitudes and z projections of the orbital, spin, and total angular momentum, respectively, define the quantum state of an atom. In the case of an atom, the angular momenta are entirely electronic in origin. This is not the case in a diatomic molecule, which may have angular momentum due to nuclear framework rotation. Furthermore, the potential energy term in an atom’s Hamiltonian is spherically symmetric, whereas this term in a diatomic molecule’s Hamiltonian has only cylindrical symmetry around the bond axis.