On this page
Why do atoms get smaller across a period even though they gain electrons? Why is fluorine so electronegative and caesium so easily ionised? Why does 4s fill before 3d? Almost every periodic trend traces back to a single idea: effective nuclear charge, the net positive charge an electron actually “feels” from the nucleus after other electrons have partly screened it. Understand this, and the periodic table stops being a list of facts to memorise and becomes a set of consequences you can predict.
The basic idea
The nucleus of an atom has a charge of +Z, where Z is the atomic number. An electron in a one-electron atom (hydrogen, or ions like He⁺) feels this full charge.
In a many-electron atom, each electron is also repelled by all the other electrons. Electrons that spend most of their time between the nucleus and the electron we’re considering partly cancel the nucleus’s attraction. This is called shielding (or screening).
The effective nuclear charge, Zeff, is:
Zeff = Z − S
where S is the shielding constant, a measure of how much the other electrons screen the nucleus.
Who shields whom?
- Inner (core) electrons shield outer electrons very effectively, because they sit between the nucleus and the outer electrons almost all the time. A core electron shields an outer electron by nearly one full unit of charge.
- Electrons in the same shell shield each other poorly, because they’re at similar distances from the nucleus and spend much of their time on different sides of it. Each contributes only about a third of a unit of shielding.
- Outer electrons barely shield inner ones at all.
A rough approximation for outer electrons: Zeff ≈ Z − (number of core electrons). For sodium: Z = 11, core electrons = 10, so Zeff ≈ 1. A more careful estimate using Slater’s rules gives about 2.2, because core shielding isn’t quite perfect.
Penetration: why s electrons feel more
Different orbitals in the same shell don’t feel the same Zeff. The key concept is penetration: how much of an orbital’s electron density lies close to the nucleus, inside the region occupied by the inner electrons.
- s orbitals penetrate the most. They have some electron density very close to the nucleus.
- p orbitals penetrate less (they have a node at the nucleus).
- d and f orbitals penetrate even less.
Electrons that penetrate further spend some time inside the shielding electrons, where they feel a larger nuclear charge. So within a shell, Zeff and stability decrease in the order s > p > d > f. This is why, in many-electron atoms, 2s is lower in energy than 2p, and 3s < 3p < 3d. See shells vs subshells vs orbitals.
Why 4s fills before 3d
In potassium, the 4s orbital, despite belonging to a higher shell, penetrates close to the nucleus, while 3d penetrates very little and is well shielded. As a result, the 4s electron feels a higher Zeff and is lower in energy than 3d, so it fills first. See the Aufbau principle.
How Zeff changes across a period
Moving left to right across a period:
- Z increases by 1 at each step.
- The added electron goes into the same shell, where it provides only a small amount of shielding (roughly 0.35 per electron).
- So Zeff on the outer electrons increases steadily, by roughly 0.65 per element.
| Period 2 element | Z | Approximate Zeff on outer electrons (Slater) |
|---|---|---|
| Li | 3 | 1.3 |
| Be | 4 | 1.95 |
| B | 5 | 2.6 |
| C | 6 | 3.25 |
| N | 7 | 3.9 |
| O | 8 | 4.55 |
| F | 9 | 5.2 |
| Ne | 10 | 5.85 |
How Zeff changes down a group
Moving down a group:
- Z increases a lot (e.g. from 3 for lithium to 11 for sodium).
- But a whole new shell of core electrons is added, shielding almost all the extra nuclear charge.
- So Zeff on the outer electron stays roughly similar (or rises only slightly).
- Meanwhile, the outer electron is in a higher shell, much further from the nucleus.
The combination of similar Zeff and greater distance means the outer electron is held less tightly down a group.
Explaining the periodic trends
Atomic radius
- Across a period: Zeff increases, pulling the outer electrons closer. Radius decreases.
- Down a group: new shells are added, and distance wins over the small change in Zeff. Radius increases.
See atomic radius trend.
Ionisation energy
- Across a period: higher Zeff and smaller radius hold the outer electron more tightly. Ionisation energy increases (with small dips explained by subshell structure).
- Down a group: the outer electron is further away and well shielded. Ionisation energy decreases.
Electronegativity and electron affinity
An atom with a high Zeff and small radius attracts bonding electrons (and extra electrons) strongly. This is why fluorine, near the top right, is the most electronegative element, and why electronegativity falls down a group. See electronegativity trend and electron affinity.
Metallic character
Low Zeff on outer electrons (bottom left of the table) means electrons are lost easily, the hallmark of metals. Caesium and francium are the most metallic elements. See most reactive metal.
Ionic radii
In an isoelectronic series such as O²⁻, F⁻, Na⁺, Mg²⁺, the electrons and their shielding are the same, but Z rises, so Zeff rises and the species shrink. See isoelectronic species.
Special effects from poor shielding
The d-block contraction
d electrons shield poorly. Across the first transition series, as 3d fills, the 4s and 4p electrons that follow feel a larger Zeff than expected. So gallium (after the d-block) is smaller than you’d predict and has a higher ionisation energy than aluminium, even though it’s below aluminium in group 13.
The lanthanide contraction
f electrons shield even more poorly. Across the lanthanides, as 4f fills, the atoms and ions shrink steadily. By the end, the elements after the lanthanides (hafnium, tantalum, tungsten…) are about the same size as the elements directly above them (zirconium, niobium, molybdenum). That’s why zirconium and hafnium are so chemically similar that they’re extremely hard to separate. See rare earth elements.
Relativistic effects in heavy atoms
In very heavy atoms such as gold, inner electrons move so fast that relativistic effects make s orbitals contract and bind more tightly. This contributes to gold’s colour and the unusually low reactivity of mercury. See why is gold yellow?
Key takeaways
- Effective nuclear charge Zeff = Z − S is the net positive charge an electron feels after shielding.
- Core electrons shield strongly; same-shell electrons shield weakly; s orbitals penetrate most and feel the highest Zeff.
- Across a period, Zeff rises, so radius falls and ionisation energy and electronegativity rise.
- Down a group, Zeff stays similar but distance increases, so outer electrons are held less tightly.
- Poor shielding by d and f electrons explains the d-block and lanthanide contractions. Calculate Zeff yourself with Slater’s rules.
Advertisement