Atomic Orbitals

An atomic orbital is a region of space around the nucleus where the probability of finding an electron is highest. Instead of moving in fixed circular paths around the nucleus, electrons exist in these regions according to the principles of quantum mechanics. The concept of atomic orbitals was developed when scientists realized that earlier atomic models, such as Bohr’s model, could not fully explain the behaviour of electrons in atoms. According to modern atomic theory, electrons behave both like particles and waves.

Each atomic orbital can hold a maximum of two electrons, and these electrons must have opposite spins. Atomic orbitals also differ in shape, size, and energy. The main types of orbitals are s, p, d, and f, and each type has a different shape and orientation.

Types of Atomic Orbitals

Atomic orbitals are regions around the nucleus where electrons are most likely to be found. These orbitals differ in shape, size, energy, and the number of electrons they can hold. Based on these characteristics, atomic orbitals are classified into four main types:

1. s Orbital

• The s orbital is the simplest type of atomic orbital.
• It has a spherical shape, which means the electron density is equally distributed in all directions around the nucleus.
• The s orbital is present in every principal energy level (n = 1, 2, 3, …).
• The size of the s orbital increases as the energy level increases.

Examples:

• Hydrogen (H) has the electron configuration 1s¹, meaning its single electron is in the 1s orbital.
• Helium (He) has the configuration 1s², meaning the 1s orbital is completely filled.

2. p Orbital

• The p orbitals appear from the second energy level (n = 2) onwards.
• They have a dumbbell shape, consisting of two lobes on opposite sides of the nucleus with a node at the nucleus.
• Each p orbital can hold 2 electrons, so the three p orbitals together can hold a maximum of 6 electrons.
• Each energy level contains three p orbitals, which are oriented along the x, y, and z axes. These are named: px, py, pz.

Examples:

• Carbon (C) has the configuration 1s² 2s² 2p², meaning two electrons occupy the 2p orbitals.
• Oxygen (O) has 2p⁴ electrons in its outer shell.

3. d Orbital

• The d orbitals appear from the third energy level (n = 3) onwards.
• These orbitals have more complex shapes, often described as cloverleaf shapes, although one of them has a slightly different shape.
• Each orbital can hold 2 electrons, so the five d orbitals together can hold a maximum of 10 electrons.
• There are five d orbitals in each energy level: dxy, dyz, dxz, dx²–y², dz².

Examples:

• Iron (Fe) has electrons in the 3d orbitals.
• Copper (Cu) and Nickel (Ni) are also elements where electrons fill the 3d orbitals.

4. f Orbital

• The f orbitals appear from the fourth energy level (n = 4) onwards.
• These orbitals have very complex shapes and are more difficult to represent compared to s, p, and d orbitals.
• There are seven f orbitals, and each can hold 2 electrons, so the f orbitals can hold a maximum of 14 electrons.

Examples:

• Lanthanide elements involve the filling of 4f orbitals (for example, cerium).
• Actinide elements involve the filling of 5f orbitals (for example, uranium).

Atomic Orbitals and Quantum Numbers

Atomic orbitals are described using quantum numbers. Quantum numbers are numerical values that help to describe the position, energy, shape, and orientation of electrons in an atom. They give complete information about the location and behavior of an electron in an atomic orbital.

There are four quantum numbers, and each one explains a different property of an electron.

1. Principal Quantum Number (n)

• The principal quantum number represents the main energy level or shell of an electron in an atom.
• It also indicates the size and energy of the orbital.
• The value of n can be 1, 2, 3, 4, and so on.

Example:
n = 1 → first energy level (1s orbital)
n = 2 → second energy level (2s, 2p orbitals)

2. Azimuthal Quantum Number (l)

• The azimuthal quantum number determines the shape of the orbital and the subshell in which the electron is present.
• The value of l ranges from 0 to (n−1).

Different values of l represent different orbitals:

• l = 0 → s orbital
• l = 1 → p orbital
• l = 2 → d orbital
• l = 3 → f orbital

3. Magnetic Quantum Number (m_l)

• The magnetic quantum number describes the orientation of an orbital in space.
• The value of mₗ ranges from −l to +l, including zero.

Example:
For p orbitals (l = 1), the possible values are −1, 0, +1, which correspond to the three p orbitals (px, py, pz).

4. Spin Quantum Number (m_s)

• The spin quantum number describes the direction of the electron's spin within an orbital.
• Each orbital can hold a maximum of two electrons with opposite spins

It has only two possible values:

• +1/2 (spin up)
• -1/2 (spin down)

Related Articles:

• Hybridization
• Molecular Orbital Theory
• Quantum Mechanical Atomic Model