Quantum Numbers

Quantum numbers can be utilized to portray the direction and the development of an electron in a particle.

What Are Quantum Numbers?

The set of numbers utilized to depict the position of an electron in a particle is called quantum numbers. There are four main quantum numbers: azimuthal, principal, spin and magnetic quantum numbers. These numbers can be characterized as a group of numerical values which give arrangements that are satisfactory by the Schrodinger wave condition for hydrogen atoms. 

The whole set of properties of a given electron in a particle is described by the four quantum numbers : 

1. Principal quantum number (represented by a letter n). 
2. Orbital precise force quantum number or azimuthal quantum number (signified by l).
3. Magnetic quantum number (indicated by ml). 
4. The electron spin quantum number (signified by ms).

Principal Quantum Number

• These numbers are signified by the letter ‘n’. Their function is to assign the foremost electron shell of an atom. They describe the most likely separation length between the core and the electrons. This means that as bigger as the central quantum number gets, the more prominent is the distance between an electron and the core of the atom (in other words, this describes the nuclear size). 
• The principal value can also be found as a greater value of 1. This value will be described by an integer number. When this value equals n=1, the number is representing the shells that are located in the most inner part of the atom. This value also represents the lower level of energy of an electron (or the lowest energy state).
• In this way, the principal quantum number should always be positive since it is not conceivable for a particle to have negative non-shell structure (it is even harder to imagine it has a negative one).
• An electron can be watched to hop from one principle shell to a higher shell, as energy is added to the system. This causes an increment of the value n. Essentially, when electrons lose vitality, they bounce back into lower shells and the value n will, consequently, decrease. 
• One phenomenon is called absorption, which explains the increment of n for an electron is called retention. During absorption, photons and energy are assimilated and retained by the electron. 
• The opposite event is called emission, in which the value n is diminished as electrons transmit energy.

Azimuthal Quantum Number (Orbital Precise Energy Quantum Number) 

• The azimuthal quantum number (known also as the orbital precise force) depicts how a given orbital is shaped. It is denoted as ‘l’ and has a value that is break-even with the overall number of precise hubs within the orbital. 
• An azimuthal quantum is a number that can be expressed either in the letter s, p, d, or f, depending on the different shapes. The value depends mainly on the quantum number value. Hence, this value can vary from 0 and (n-1). 
• For instance, if this value equals n =3, the azimuthal quantum number will range from 0 to n-1. If l=0, the subshell will be, consequently ‘s’. Conversely, if l=1 and l=2, subshells will be ‘p’ and ‘d’. Consequently, if  n=3, there will be three conceivable subshells: 3s, 3p, and 3d. 
• Another example is a value of n is 5, where l can take a value 0, 1, 2, 3, and 4.

Magnetic Quantum Number

After adding up the number of orbitals in a subshell and how those are oriented, depending on what we call the Magnetic Quantum Number. This number is represented by the image ‘ml’ and it yields the projection of the precise energy compared to the orbital along with a given hub.

The value of azimuth (also called the angular moment) affects the quantum number, the value of l and that of ml varies in an interval range of -l to +l. 

One example is shown below:

In case n = 4 and l = 3, the magnetic quantum number can take values of -3, -2, -1, 0, +1, +2, and +3.

The total number of orbitals in a given subspace behaves as a function of the value of “l”. The function defining this relationship is given by the formula (2l + 1). To analyze this in detail, let us consider the following example. In the “3d” subshell, where n can take values of 3 and 2, there are 5 orbitals (this is explained as 2*2 + 1). In each orbital, 2 electrons can be found. This means that the 3d subshell can hold up to 10 electrons.

In the following table, you can understand the relations in subshells depending on the value of the azimuthal number, the number of orbitals and the possible m1 from these combinations.