Difficulty: Introductory | Prerequisites: Quantum numbers and atomic orbitals (see companion notes)
Once you know what orbitals look like and how quantum numbers label them, the next question is: in what order do electrons fill those orbitals? This section covers the three rules that govern filling order (Aufbau, Pauli, Hund's), then introduces effective nuclear charge and ionisation energy, two concepts that explain periodic trends. These trends drive reactivity in organic chemistry, so understanding them now saves time later when you reach electronegativity, acidity, and nucleophilicity.
Electrons fill the lowest-energy orbitals first (Aufbau), no two electrons can share the same quantum state (Pauli), and electrons spread out across orbitals of equal energy before pairing up (Hund's). Effective nuclear charge (Zeff) measures how strongly the nucleus pulls on a given electron after accounting for shielding, and it drives periodic trends in ionisation energy.
Aufbau principle
In the ground state of an atom or ion, electrons fill subshells in order of increasing energy, starting from the lowest. Think of it as filling seats from the front row of a theatre before moving to the back.
Pauli exclusion principle
No two electrons in an atom can have the same set of four quantum numbers. In practical terms, this means each orbital holds at most two electrons, and those two must have opposite spins (+1/2 and -1/2).
Hund's rule
When filling orbitals of the same energy (degenerate orbitals), electrons occupy them singly first, all with the same spin, before any orbital gets a second electron. In simple terms, electrons prefer their own space and spread out before doubling up.
Effective nuclear charge (Zeff)
The net positive charge experienced by a particular electron after accounting for shielding by inner electrons. Calculated as Zeff = atomic number minus the number of core (inner-shell) electrons. Think of it as how strongly the nucleus "pulls" on a valence electron once you factor in the electrons blocking its view.
Ionisation energy (ionization energy)
The energy required to remove one electron from a neutral atom in the gas phase. Higher ionisation energy means the atom holds its electrons more tightly.
Coulomb's law
The electrostatic force between two charged particles is proportional to the product of their charges and inversely proportional to the square of the distance between them. This is the physics behind why Zeff and distance from the nucleus together determine how tightly an electron is held.
Shielding (screening)
The reduction in nuclear attraction experienced by outer electrons because inner electrons repel them and partially block the nuclear charge. More inner electrons means more shielding, which lowers Zeff for the outer electrons.
Aufbau principle: Electrons fill subshells from lowest energy to highest. The standard filling order is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, and so on. In the ground state, no higher-energy subshell is occupied until the lower ones are full.
Pauli exclusion principle: Two electrons in the same orbital must have opposite spins. This caps every orbital at two electrons. If two electrons share an energy level and orbital type (same n, l, and m_l), their spin quantum numbers must differ.
Hund's rule: For a set of degenerate orbitals (same energy), electrons fill each orbital singly before any orbital receives a second electron. All singly occupied orbitals have electrons with the same spin direction. This minimises electron-electron repulsion.
The nucleus has a positive charge equal to the atomic number (Z). Inner-shell electrons shield outer electrons from the full nuclear pull.
Zeff gives a simple estimate of the net charge felt by a valence electron.
Quick calculation: Zeff = Z (atomic number) minus the number of core electrons (approximated as the atomic number of the preceding noble gas).
Example: sodium (Na), Z = 11. The preceding noble gas is neon (Z = 10). Zeff for a valence electron of Na = 11 - 10 = 1.
Example: chlorine (Cl), Z = 17. Preceding noble gas is neon (Z = 10). Zeff = 17 - 10 = 7.
Zeff is the single most important factor in determining the "personality" of each element, meaning its reactivity, size, and tendency to gain or lose electrons.
The force between the nucleus and an electron follows Coulomb's law: F = k(q1 * q2) / r², where q1 and q2 are the charges and r is the distance between them.
A negative force value indicates attraction (opposite charges).
The force drops off with the square of the distance, so electrons farther from the nucleus are held much less tightly.
Since the electron charge is constant, the strength of the interaction depends primarily on nuclear charge (Zeff) and distance (which shell the electron occupies).
Ionisation energy is the energy needed to remove one electron from a neutral gas-phase atom.
Across a period (left to right): ionisation energy increases because Zeff increases while the valence electrons are in the same shell. The nucleus pulls harder without a corresponding increase in shielding.
Down a group (top to bottom): ionisation energy decreases because the valence electrons are in higher shells, farther from the nucleus, even though Z is larger. The increased distance and additional shielding outweigh the higher nuclear charge.
Zeff reaches its maximum at the noble gas configuration within each period. This is one reason noble gases are so stable and is a foundation for the octet rule.
Coulomb's law: F = k(q1 * q2) / r²
Effective nuclear charge (simplified): Zeff = Z - S, where Z is the atomic number and S is the number of core electrons (roughly the atomic number of the preceding noble gas)
Max electrons per shell: 2n²
Ionisation energy trends explain why metals on the left side of the periodic table lose electrons so readily, which is why sodium reacts violently with water while neon does nothing. Effective nuclear charge is the concept behind electronegativity differences that drive polarity in organic molecules, ultimately determining solubility, boiling points, and how reactions proceed.
Students often assume Zeff is the same as the atomic number. It is not. Zeff accounts for shielding by inner electrons, so it is always less than Z for any electron that is not in the 1s orbital.
A common error is thinking that ionisation energy always increases with atomic number. It does not. Moving down a group, ionisation energy decreases even though Z increases, because the added distance and shielding matter more.
Students sometimes apply Hund's rule to orbitals of different energies. Hund's rule applies only to degenerate orbitals (orbitals at the same energy level within the same subshell).
Some students confuse ionisation energy with electron affinity. Ionisation energy is about removing an electron; electron affinity is about gaining one.
Writing electron configurations using Aufbau, Pauli, and Hund's rule is a near-certain exam question. Be able to write the full configuration and orbital diagram for any element in the first four periods.
Expect questions asking you to calculate Zeff for a given element and explain how it relates to periodic trends.
Ionisation energy trend questions (across a period, down a group) are standard. Be ready to explain the trend using both Zeff and distance.
The connection between Zeff reaching a maximum at noble gases and the octet rule is a conceptual favourite on exams.
True or false: according to the Aufbau principle, the 3d subshell fills before the 4s subshell.
Fill in the blank: Hund's rule states that electrons occupy degenerate orbitals ______ before pairing up.
What is the Zeff for a valence electron of fluorine (Z = 9)?
True or false: ionisation energy increases as you move down a group in the periodic table.
According to the Pauli exclusion principle, what is the maximum number of electrons in a single orbital?
Answers: 1. False (4s fills before 3d in the standard filling order). 2. Singly (with parallel spins). 3. Zeff = 9 - 2 = 7 (preceding noble gas is He, Z = 2). 4. False (it decreases). 5. Two.
Q: Write the full electron configuration for phosphorus (Z = 15) and identify which rule determines the arrangement of electrons in the 3p orbitals.
A: 1s² 2s² 2p⁶ 3s² 3p³. Hund's rule determines that the three 3p electrons each occupy a separate p orbital with parallel spins before any pairing occurs.
Q: Explain why sodium (Na) has a much lower ionisation energy than neon (Ne), even though Na has a higher atomic number.
A: Sodium's valence electron is in the 3s subshell, a new shell beyond the filled second shell. It experiences a Zeff of about 1 (11 - 10), while neon's valence electrons are in the 2p subshell with a much higher Zeff. The combination of lower Zeff and greater distance from the nucleus makes sodium's electron far easier to remove.
Q: Using Coulomb's law, explain why the force between the nucleus and a 1s electron is stronger than the force between the nucleus and a 3s electron in the same atom.
A: Coulomb's law says force is inversely proportional to the square of the distance. A 1s electron is much closer to the nucleus than a 3s electron, so the electrostatic attraction is far greater. The 3s electron also experiences more shielding from the inner electrons, further reducing the effective force.
Q: Why does Zeff reach a maximum at the noble gas configuration within each period?
A: Moving across a period, each additional proton increases the nuclear charge, but the added electrons go into the same shell and provide relatively little additional shielding for one another. By the time you reach the noble gas, Z has increased substantially while the core electron count has stayed the same, so Zeff is at its highest.
Effective nuclear charge and ionisation energy connect directly to electronegativity (Chapter 1.2), which governs bond polarity and molecular dipoles. The electron configuration rules here also underpin how atoms form bonds: sigma and pi bonding rely on which orbitals are occupied and available. Ionisation energy trends reappear when you study acid-base chemistry, because a species that loses electrons easily also tends to stabilise positive charge.
Aufbau principle, Pauli exclusion principle, Hund's rule, electron configuration, orbital filling order, effective nuclear charge, Zeff, shielding, screening, Coulomb's law, electrostatic force, ionisation energy, ionization energy, periodic trends, noble gas configuration, octet rule, core electrons, valence electrons, degenerate orbitals, electron-electron repulsion, organic chemistry chapter 1.1, Purdue organic chemistry