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Home / Chemistry / Atomic Orbitals - Understanding Quantum Numbers & Their Types

Atomic Orbitals - Understanding Quantum Numbers & Their Types

Last Updated on Feb 18, 2025
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The Basics of Atomic Orbitals

Let's delve into the world of atoms! Specifically, let's explore atomic orbitals, which are mathematical functions that shed light on the wave-like behavior of electrons (or pairs of electrons) surrounding atomic nuclei. These functions are crucial in quantum mechanics and atomic theory, as they help us predict the likelihood of finding an electron in a specific region around the atom's nucleus.

It's worth noting that 'atomic orbital' can also refer to the physical space around an atom’s nucleus where there's a high probability of finding a particular electron. This physical region is defined by the atomic orbital's mathematical function.

Each atomic orbital is unique, and its characteristics depend on the values of the following quantum numbers :

  • The principal quantum number (symbolized as ‘n’)
  • The azimuthal quantum number, also known as the orbital angular momentum quantum number (symbolized as ‘l’)
  • The magnetic quantum number (symbolized as ‘m l ’)

Additionally, each atomic orbital can accommodate a maximum of two electrons. In fully occupied atomic orbitals (those containing two electrons), the electrons have opposite spins. The spin quantum number, symbolized as ‘m s ’, provides insight into an electron's spin. Therefore, we can learn more about any electron in any atomic orbital within an atom by determining the values of these four quantum numbers.

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Atomic Orbitals: Names and Quantum Number Relationships

Atomic orbitals are typically named using a combination of the principal quantum number (n) and the azimuthal quantum number (l). Here are the simple names of atomic orbitals and their corresponding azimuthal quantum numbers:

  • The s orbital (azimuthal quantum number = 0)
  • The p orbital (azimuthal quantum number = 1)
  • The d orbital (azimuthal quantum number = 2)
  • The f orbital (azimuthal quantum number = 3)
  • The g orbital (azimuthal quantum number = 4)
  • The h orbital (azimuthal quantum number = 5)

The naming of atomic orbitals follows the alphabet, skipping the letter ‘j’ to avoid confusion in languages that don't distinguish between ‘j’ and ‘i’. Therefore, an atomic orbital with l=6 is named ‘i’, and with l=7, it's named ‘k’. Interestingly, the names of the first four orbitals (s, p, d, and f) come from the terms spectroscopists used to describe the spectroscopic lines of alkali metals: 'sharp', 'principal', 'diffuse', and 'fundamental'.

When naming a specific atomic orbital, we add the value of the principal quantum number as a prefix to the alphabetical name of the azimuthal quantum number. The value of the azimuthal quantum number depends on the value of the principal quantum number. For any given value of ‘n’, the value of ‘l’ can range from zero to (n-1). For instance, if ‘n’ equals 3, ‘l’ can be 0, 1, or 2. Thus, the atomic orbitals are named 3s (n=3, l=0), 3p (n=3, l=1), and 3d (n=3, l=2). It's worth noting that a 3f orbital cannot exist because that would require ‘n’ and ‘l’ to both equal 3, which is impossible since the value of the azimuthal quantum number must always be less than that of the principal quantum number.

A Table of All Possible Atomic Orbitals with ‘n’ Ranging from 0 to 5

Value of the Principal Quantum Number (n) Possible Values of the Azimuthal Quantum Number (l) Names of all Possible Atomic Orbitals for Given Value of ‘n’
1
  • l = 0 (s orbital)
  • The 1s orbital
2
  • l = 0 (s orbital)
  • l = 1 (p orbital)
  • The 2s orbital
  • The 2p orbital
3
  • l = 0 (s orbital)
  • l = 1 (p orbital)
  • l = 2 (d orbital)
  • The 3s orbital
  • The 3p orbital
  • The 3d orbital
4
  • l = 0 (s orbital)
  • l = 1 (p orbital)
  • l = 2 (d orbital)
  • l = 3 (f orbital)
  • The 4s orbital
  • The 4p orbital
  • The 4d orbital
  • The 4f orbital
5
  • l = 0 (s orbital)
  • l = 1 (p orbital)
  • l = 2 (d orbital)
  • l = 3 (f orbital)
  • l = 4 (g orbital)
  • The 5s orbital
  • The 5p orbital
  • The 5d orbital
  • The 5f orbital
  • The 5g orbital

Remember, electrons fill these orbitals according to certain rules, such as the Aufbau principle , the Pauli exclusion principle, and Hund’s rule of maximum multiplicity.

More Articles for Chemistry

Frequently Asked Questions

There are four types of orbitals that you should know (sharp, principal, diffuse and fundamental) with s, p, d and f. Few variations of orbitals occur within each shell of an atom.

An atomic orbital is a mathematical term in atomic theory and quantum mechanics that describes the position and wavelike behaviour of an electron in an atom. A maximum of two electrons, each with its own spin quantum number s, will occupy each of those orbitals.

Orbital, a mathematical term in chemistry and physics, called a wave function, which defines the characteristic properties of no more than two electrons, as in a particle, in the proximity of an atomic nucleus or system of nuclei.

The positions surrounding an atom’s nucleus where the electrons are most likely to be at any given moment are atomic orbitals. It is a mathematical feature that defines either one electron or a pair of electrons’ wave-like behaviour in an atom.

Electrons occupy orbitals of low energy (closer to the nucleus) until they enter those of higher energy. If there is a choice of equal-energy orbitals, as far as possible, they fill the orbitals independently. Where appropriate, this filling of orbitals alone is known as Hund’s law.
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