Order of Filling Shells

Introduction

The arrangement of electrons in an atom determines nearly every property of an element — from how it reacts chemically to where it appears in the periodic table. To understand this arrangement, one must understand the order in which electrons fill atomic shells.

Electrons do not fill the energy levels of an atom randomly. They occupy specific shells and subshells according to certain principles that minimize the atom’s energy. The process of filling these shells follows a definite sequence: first K, then L, then M, then N, and so on.

This concept is not merely a rule of thumb; it is rooted deeply in the quantum mechanical nature of matter. The way electrons fill shells is governed by their energy levels, stability requirements, and fundamental principles of quantum mechanics such as the Aufbau principle, the Pauli exclusion principle, and Hund’s rule.

This comprehensive discussion will explain the order of filling shells, why electrons prefer the lowest energy levels first, how this order is determined, and how it influences the chemical behavior of elements.

Understanding Atomic Structure

Every atom is composed of a nucleus, containing protons and neutrons, surrounded by electrons moving in defined energy levels or shells. These shells are often visualized as concentric circles around the nucleus, though in quantum mechanics, they are actually regions of probability known as orbitals.

Each shell corresponds to a specific principal quantum number (n).

The first shell (K-shell) corresponds to n = 1.
The second shell (L-shell) corresponds to n = 2.
The third shell (M-shell) corresponds to n = 3.
The fourth shell (N-shell) corresponds to n = 4, and so on.

These shells represent increasing energy levels. Electrons in the K-shell are closest to the nucleus and possess the lowest energy, while those in outer shells have higher energy.

However, the way electrons fill these shells is not simply based on the order of n = 1, 2, 3, 4. Instead, it depends on the relative energy of orbitals, which is influenced by both the principal quantum number (n) and the azimuthal quantum number (l).

The Quantum Mechanical Foundation

In quantum mechanics, each electron in an atom is described by a set of four quantum numbers that define its energy, shape, orientation, and spin.

Principal Quantum Number (n): Indicates the main energy level or shell.
Azimuthal Quantum Number (l): Describes the shape of the orbital (s, p, d, or f).
Magnetic Quantum Number (m): Determines the orientation of the orbital in space.
Spin Quantum Number (s): Specifies the direction of electron spin (+½ or –½).

The energy of an orbital depends on both n and l, not just n alone. This means that orbitals from different shells can overlap in energy. For example, the 4s orbital has slightly lower energy than the 3d orbital.

This overlap is the reason why the order of filling is not always linear from K to L to M in terms of n, but rather follows a pattern based on increasing energy.

The Aufbau Principle

The word Aufbau comes from German, meaning “building up.” The Aufbau Principle states that:

“Electrons occupy the lowest energy orbital available before filling higher energy orbitals.”

This principle provides the foundation for determining the order of electron filling. According to it, electrons enter the lowest possible energy level first to make the atom as stable as possible.

For instance, in a hydrogen atom (which has only one electron), the electron occupies the 1s orbital — the lowest energy orbital. In helium (two electrons), both electrons occupy the 1s orbital, fully filling it. Only when this orbital is full do additional electrons begin to fill the next higher orbital, the 2s orbital.

This process of sequential filling continues for all elements in the periodic table.

The Pauli Exclusion Principle

Proposed by Wolfgang Pauli in 1925, the Pauli Exclusion Principle states that:

“No two electrons in an atom can have the same set of four quantum numbers.”

This principle limits the number of electrons that can occupy each orbital. Since an orbital can hold only two electrons with opposite spins, once an orbital is full, any additional electrons must move to a higher-energy orbital.

This is why, after the 1s orbital is filled with two electrons, the next electrons must enter the 2s orbital, and so on.

Hund’s Rule of Maximum Multiplicity

Hund’s Rule states that:

“Electrons fill degenerate orbitals (orbitals of equal energy) singly first, with parallel spins, before pairing up.”

For example, the three 2p orbitals (2px, 2py, 2pz) have the same energy. If there are three electrons to be placed in these orbitals, each will occupy a separate orbital rather than pairing up in one.

This rule minimizes electron-electron repulsion and leads to greater stability.

The Energy Levels and Subshells

Each shell is divided into subshells, which are designated by letters according to the azimuthal quantum number (l):

Subshell	Value of l	Type of Orbital	Maximum Electrons
s	0	Spherical	2
p	1	Dumbbell-shaped	6
d	2	Complex shape	10
f	3	More complex	14

Thus, each shell can have different subshells depending on its principal quantum number (n).

For example:

When n = 1 → only s subshell → 1s
When n = 2 → s and p subshells → 2s, 2p
When n = 3 → s, p, and d subshells → 3s, 3p, 3d
When n = 4 → s, p, d, and f subshells → 4s, 4p, 4d, 4f

The order in which these subshells are filled depends on their energy, not simply on n.

The Order of Filling Orbitals

By combining the Aufbau principle, the Pauli exclusion principle, and Hund’s rule, scientists have determined the order in which electrons fill orbitals.

This order is based on increasing energy levels of the orbitals and is represented as follows:

1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p

This sequence is often remembered using the diagonal rule or Aufbau chart, which visually shows how orbitals fill based on increasing energy.

The Shell Filling Order: K, L, M, N, and Beyond

The simplest way to understand the filling of shells is to consider them by their shell names.

Shell	Principal Quantum Number (n)	Subshells Included	Maximum Electrons (2n²)
K	1	1s	2
L	2	2s, 2p	8
M	3	3s, 3p, 3d	18
N	4	4s, 4p, 4d, 4f	32

Electrons fill these shells in increasing order of energy. The K-shell is filled first because it is closest to the nucleus and has the lowest energy. Once it is full, electrons move to the L-shell, then M-shell, and so forth.

However, due to energy overlaps between subshells, the actual order of filling sometimes involves orbitals from higher shells being filled before lower ones (for example, 4s before 3d).

Understanding Why Electrons Fill the Lowest Energy Level First

Atoms naturally seek the most stable configuration. Stability in atomic structure comes from having the lowest possible energy.

Filling lower-energy orbitals first achieves this stability.

When an electron occupies a lower energy level, the atom’s total energy decreases, making it more stable. If an electron were to occupy a higher energy orbital while a lower one is still empty, the atom would have unnecessary energy and therefore be unstable.

This is why electrons always fill the lowest available energy level before moving to higher levels.

Examples of Shell Filling in Different Elements

Example 1: Hydrogen (Atomic Number 1)

Total electrons = 1
Filling order: 1s¹
Only the K-shell (n = 1) is occupied.

Example 2: Helium (Atomic Number 2)

Total electrons = 2
Filling order: 1s²
K-shell is completely filled; atom is stable.

Example 3: Lithium (Atomic Number 3)

Total electrons = 3
Filling order: 1s² 2s¹
K-shell is full, and the remaining electron enters the L-shell.

Example 4: Neon (Atomic Number 10)

Total electrons = 10
Filling order: 1s² 2s² 2p⁶
K-shell and L-shell are completely filled.

Example 5: Calcium (Atomic Number 20)

Total electrons = 20
Filling order: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s²
The 4s orbital (in the N-shell) fills before 3d because it has slightly lower energy.

These examples show that electrons fill orbitals in order of increasing energy — starting from the lowest.

The Diagonal Rule

The diagonal rule is a simple way to remember the order in which orbitals are filled. It is written as a series of diagonal arrows that show the path electrons take as energy increases.

When you list the orbitals as below and draw diagonals from top right to bottom left, you can easily see the filling order:

1s  
2s  2p  
3s  3p  3d  
4s  4p  4d  4f  
5s  5p  5d  5f  
6s  6p  6d  
7s  7p

Following the diagonal arrows gives:
1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p

This sequence reflects the order of increasing energy levels and corresponds to the actual filling of shells in atoms.

The Connection to the Periodic Table

The order of shell filling is directly related to the structure of the periodic table. Each period of the table corresponds to the filling of a new principal energy level.

Period 1: Filling of 1s (K-shell) → Hydrogen, Helium
Period 2: Filling of 2s and 2p (L-shell) → Lithium to Neon
Period 3: Filling of 3s and 3p (M-shell) → Sodium to Argon
Period 4: Filling of 4s and 3d (N-shell begins) → Potassium to Krypton

As we move across each period, electrons are added to orbitals in the order determined by energy. This is why elements in the same group have similar chemical properties — they share the same outer-shell electron configuration.

Stability and the Octet Rule

The concept of shell filling also leads to the octet rule, which states that atoms tend to gain, lose, or share electrons to achieve eight electrons in their outermost shell.

This rule explains why noble gases (like neon and argon) are stable — their outer shells are completely filled. In contrast, other elements react to achieve a similar configuration.

The filling order ensures that electrons occupy shells in a way that helps atoms approach this stable arrangement.

Exceptions in the Filling Order

While the 2n² rule and Aufbau principle provide a general pattern, there are exceptions due to energy similarities between orbitals.

For example:

Chromium (Cr, Z = 24): Expected configuration = [Ar] 4s² 3d⁴
Actual configuration = [Ar] 4s¹ 3d⁵ (half-filled d-subshell gives extra stability).
Copper (Cu, Z = 29): Expected configuration = [Ar] 4s² 3d⁹
Actual configuration = [Ar] 4s¹ 3d¹⁰ (fully filled d-subshell is more stable).

These exceptions show that while the general order of filling shells is reliable, stability can sometimes cause deviations.

Energy Diagrams

An energy-level diagram visually represents the order of filling. The orbitals are arranged vertically according to energy, and arrows representing electrons are placed in them according to the rules discussed.

For example, for nitrogen (Z = 7):

1s² 2s² 2p³

In the diagram, the 1s and 2s orbitals are fully filled, and the three electrons in 2p are arranged singly in three orbitals following Hund’s rule.

This visualization helps explain how electrons occupy the lowest available orbitals first, moving upward only when necessary.

Why Understanding the Order of Filling Matters

Predicting Electron Configurations: Knowing the filling order helps determine how electrons are distributed in atoms.
Explaining Chemical Behavior: The outermost electrons dictate bonding and reactivity.
Understanding the Periodic Table: The structure of the table directly follows orbital filling patterns.
Studying Spectra: Energy transitions between orbitals produce atomic spectra.
Exploring Quantum Mechanics: The filling order reveals how energy quantization governs atomic structure.

Summary of Rules for Filling Shells

Electrons fill orbitals in order of increasing energy (Aufbau principle).
Each orbital can hold a maximum of two electrons (Pauli exclusion principle).
Degenerate orbitals are singly occupied before pairing (Hund’s rule).
Filling follows the sequence:
1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p.
Shells fill in the order K → L → M → N, with energy considerations causing minor overlaps.