Relationship between Atomic Orbitals and Quantum Numbers

Quantum numbers are a set of four parameters that describe the unique quantum state of an electron in an atom. These numbers arise from the solution of the Schrödinger equation for the hydrogen atom and provide a rule for understanding the electronic structure of atoms. Each electron in a orbital has four quantum numbers. These are discussed below:

Four Quantum Numbers

1. Principal Quantum Number (n): Denoted by “n”, it determines the energy level of an electron and the size of the orbital. It can take integer values starting from 1 (1, 2, 3, …).

2. Azimuthal Quantum Number (l): It is denoted as ‘l’, and defines the shape of the orbital. It takes value from from 0 to (n − 1). The azimuthal quantum number for different atomic orbitals are s (l = 0), p (l = 1), d (l = 2), f (l = 3), and so on.

3. Magnetic Quantum Number (m_l): It is denoted as “m_l”. It refers to the direction of the orbital in space. It takes value from -l to l.

4. Spin Quantum Number (m_s): It is denoted as “m_s” which defines the spin of electrons in a room or the angular momentum of electrons. It takes the value +1/2 or -1/2, which indicates electron spin states.

Rules for Relationship between Quantum Numbers and Atomic Orbitals

1. Pauli Exclusion Principle: It states that no two electrons can have all the four quantum numbers same.

2. Quantization of Angular Momentum: The component of the angular momentum quantum number only takes integer values from 0 to (n-1) with no value in between them.

3. Magnetic Quantum Number and Angular Momentum: The values of the magnetic quantum number “m_l” can be negative, zero, or positive, being equal to -l, 0, and +l. This means there will be 2l+1 possible values of m_l

4. Spin-Orbit Coupling: Spin-orbit coupling is a quantum mechanical interaction that arises from the coupling between an electron’s intrinsic spin angular momentum and its orbital angular momentum due to the presence of an external electromagnetic field. It is is responsible for the splitting of spectral lines in atoms into multiple closely spaced lines, known as fine structure.

The quantum numbers and the relationships between them are very important for the understanding of electron behavior—electrons in atoms and molecules, mainly the inner states and configurations of electrons within the overall system.

Table for Relation between Quantum Numbers and Atomic Orbital

The relation between Quantum Numbers and Atomic Numbers are discussed in the following table

Atomic orbitals are regions around the nucleus of an atom where electrons are likely to be found. They are described by quantum mechanics and are characterized by specific quantum numbers. Each type of atomic orbital has a distinct shape, size, and orientation, which corresponds to the probability distribution of finding an electron within that orbital.

In this article, we will learn in detail about atomic orbitals, their names, definition, significance and how they are related to different quantum numbers.