Atomic Orbitals and Quantum Numbers

The Bohr model was one of the one-dimensional models used to describe electron distribution in a quantum. In this case, the n quantum number was the sole piece of information that mattered. Because of Schrodinger’s equation, the electron was able to captivate three-dimensional space. A three-quantum number description of electron orbitals was therefore required to explain them.

Quantum Numbers and Atomic Orbitals

The Quantum Numbers are a set of four numbers that describe the relationship between an electron and the nucleus. The energy (Principle quantum number), shape (Angular momentum quantum number), and orientation of the orbital are described by the first three numbers (magnetic quantum number). The fourth number represents the electron’s “spin” (spin quantum number).

The energy of an electron and the most likely distance of the electron from the nucleus are described by the principal quantum number, n. In other words, it refers to the size of an electron’s orbital and the energy level it occupies. The shape of the orbital is described by the number of subshells or l.

Quantum Number Principle (n)

The principal quantum number describes the orbital distance from the nucleus. Higher n values result in electrons being further away. Because electrons are negatively charged, those closest to the positively charged nucleus are more powerfully attracted and tightly bound than those further away. Electrons in close proximity to the nucleus.

As a result, they’re more stable, and the atom is less likely to lose them. In other words, as n increases, the energy of the electron increases, as does the likelihood of the atom losing that electron. A shell is made up of all the atomic orbitals with the same n in a given atom. The integer value of n can be 1 or higher.

Quantum Number of Angular Momentum (l)

The shape of the orbital is described by the angular momentum quantum number. A number or a letter can be used to represent the angular momentum number (or subshell).

The magnetic quantum number (m) indicates the orbital’s orientation in space; in other words, the value of m indicates whether an orbital is aligned with the x-axis.

The nucleus of the atom is at the origin of the x-, y-, or z-axis on a three-dimensional graph. M can have any value between -l and +l. For our purposes, it’s only important that this quantum number tells us that there could be one s-orbital, three p-orbitals, five d-orbitals, and so on for each value of n.

Shells and Subshells of Orbitals

The level of the principal electron shell is determined by the value of the principal quantum number n (principal level). The principal level is shared by all orbitals with the same n value. 

Subshells 

The number of orbital angular number l values can also be used to determine the number of subshells in a principal electron shell:

When n equals 1, l equals 0. 

When n=2 and l=0, 1 (l takes on two values, and thus there are two possible subshells)

When n=3 and l=0, 1, 2, (l takes on three values, and thus there are three possible subshells)

Orbitals

A subshell’s number of orbitals corresponds to the number of possible values for the magnetic quantum number “ml”. (2l +1) is a useful equation for determining the number of orbitals in a subshell.

Azimuthal Quantum Number-

The azimuthal (or the orbital angular instigation) quantum number is defined as the determination of the shape of an orbital. Its value is equal to the total number of angular bumps in the orbital and is indicated by the symbol l.’

The azimuthal quantum number can suggest an s, p, d, or f subshell, all of which have different forms. This value is determined by (and limited by) the primary account number, i.e. the azimuthal quantum number varies between 0 and 1. 

Conclusion:

For illustration, if n = 3, the azimuthal quantum number can be 0, 1, or 2. The performing subshell is a subshell when l = 0. When l = 1 and l = 2, the performing subshells are p and d subshells, independently. In another illustration, the possible values of l are 0, 1, 2, 3, and 4 when the value of n is 5. There are three angular bumps if l = 3.