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Introduction
According to quantum mechanics, electrons don’t orbit the nucleus like planets around a star. Particles of subatomic sizes exist in multiple places at once until you measure them. Therefore, it is more fitting to interpret that electrons exist in regions of probability called orbitals, which highlight the places you would most likely find them at.
Electron configuration tells us where electrons are located in an atom. Understanding how electrons fill these orbitals is crucial for electron configuration.
There are four quantum numbers that govern where an electron is located around a nucleus:
The Principal Quantum Number (n) indicates the relative distance between an electron and the nucleus. The higher the number, the farther away an electron is.
n = 1, 2, 3…
Each ring on the Bohr model clearly represents the principal quantum numbers.
The electrons with the greatest principle number are valence electrons.
Angular Momentum Number (l) determines the shape of an orbital.
If l = 0, the electron belongs in a s-orbital shell (sphere).
If l = 1, the electron belongs in a p-orbital shell (dumbbell).
If l = 2, the electron belongs in a d-orbital shell (clover).
If l = 3, the electron belongs in a f-orbital shell (complex).
Magnetic Quantum Number (ml) tells us the orientation of the orbital.
It ranges from -l to +l.
For example: If an electron has an angular momentum of l = 1, then ml = -1, 0, +1. Therefore, there are 3 possible orientations for p-orbitals.
Spin Quantum Number (mₛ) describes an electron’s “spin.” (intrinsic angular momentum)
Momentum of a charge creates magnetism. However, the electron isn’t actually spinning, as it would have to rotate faster than the speed of light to create the magnetism. We just know that this property exists because electrons are responsible for magnetism in certain materials, hence the name intrinsic angular momentum.
mₛ = +½ or -½
There are two electrons per orbital. Due to stability, paired electrons cannot possess the same spin numbers, so they must have opposite spin for the magnetism to cancel out.
Simple Visualization of Orbital Types
Electrons fill orbitals in a predictable order, governed by these rules:
Aufbau Principle: Electrons fill the lowest energy orbitals available before moving to higher ones.
Order of subshells: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, and so on.
Hold on… why does 3d (a n=3 subshell) fill after 4s?
According to the Madelung rule, the energy level is calculated by (n + l).
4s has n=4 and l=0.
3d has n=3 and l=2.
(4+0) < (3+2), so 3d has a higher energy level.
Conceptually, this happens because the inner 3s and 3p orbitals form a stable inner octet, so the 3d orbitals get pushed out more due to repulsion.
Pauli Exclusion Principle: No two identical fermions (particles with half-integer spins, like electrons) can occupy the same quantum state (e.g. quantum numbers) within a quantum system (e.g. orbitals).
This principle keeps spin numbers opposite.
Hund’s Rule: When filling a subshell, electrons spread out and occupy all possible orientations of the subshell before pairing.
All of these rules make sure electrons occupy orbitals in the most stable way, maximizing attraction to the nucleus while minimizing repulsion between electrons.
STABILITY RULES:
Full Valence Shell: Atoms or ions are the most stable when the outermost s and p subshells are full, because a full electron configuration is the most energetically favorable.
Full Subshell: Atoms or ions with full outermost subshells (e.g. ending with 2s², ending with 3p⁶) are more stable than partially-filled subshells, because it maximizes electron pairing while minimizing repulsion.
Half-Filled Subshells: Atoms or ions with half-filled outermost subshells (e.g. ending with 3s¹, ending with 4p³) are more stable than other partially-filled subshells, because all the electrons are symmetrically arranged with the outermost electrons occupying their own orbitals, minimizing repulsion.
Each subshell is labelled as n(shell type)ˣ.
n is the principal quantum number
Shell Types: s, p, d, f
x means how much electrons per subshell
Writing Electron Configuration
Now that we have reviewed the basics of electron configuration, let’s name the electron configurations of some elements and ions.
Each subshell is labelled as n(shell type)ˣ.
n is the principal quantum number
Shell Types: s, p, d, f
x means how much electrons per subshell
To make the process easier, we can label the periodic table in blocks. We then progress from left to right, downwards.
Carbon: 1s² 2s² 2p²
Gallium: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p¹
Ion Electron Configuration: If we got our hands on some salt, made of sodium and chloride ions, what are their configurations like?
The sodium ion lost one electron to achieve the nearest stable configuration, the same as a neutral neon atom: 1s² 2s² 2p⁶
The chloride ion gained one electron to achieve the nearest stable configuration, the same as a neutral argon atom: 1s² 2s² 2p⁶ 3s² 3p⁶
Some elements don't strictly use valence electrons for reactions:
Examples:
Iron: It has two valence electrons (config: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶). However, its most common oxidation state is +3 because it will rather use its two 4s electrons (easiest to lose) and one 3d electron (to create a half 3d subshell).
Titanium: It has two valence electrons (config: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d²). However, its most common oxidation state is +4 because it will rather use its two 4s electrons (easiest to lose) and two 3d electrons (to empty 3d subshell and expose full 3p subshell).
Some elements don't follow the standard ordering for electron configuration:
Examples:
Chromium: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵, an electron from 4s goes to 3d to create two half-filled subshells.
Copper: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d¹⁰, an electron from 4s goes to 3d to create a half-filled 4s subshell and a full 3d subshell.
Examples of Noble Gas Configuration Shortcuts
As a shortcut, you could add onto the configurations of Group 18 elements for atoms or ions that surpass those configurations. Basically, you substitute all the configurations that match the previous Group 18 element and move on.
Oxygen (O): [He] 2s² 2p⁴
Phosphorus (P): [Ne] 3s² 3p³
Zinc (Zn): [Ar] 4s² 3d¹⁰
Orbital Diagram Examples
Each box represents an orbital. Boxes packed close together represent a subshell.
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