Worked example 1
Estimate Zeff for a valence electron in sodium (Z = 11) and in chlorine (Z = 17), and say what the comparison predicts.
Try it first: Count core electrons for each before doing any subtraction.
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Periodic TrendsEffective nuclear chargeContent level: Core 20 min
Shielding and Effective Nuclear Charge
What you'll be able to do: Estimate effective nuclear charge and use it to explain why every periodic trend behaves the way it does.
Best after: Electron Configurations and Orbital Filling
Introduction
Every trend in this unit reduces to one competition: how strongly the nucleus pulls on an outer electron, and how much the inner electrons get in the way. Effective nuclear charge is the number that captures that competition.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Define shielding and effective nuclear charge
- Estimate Zeff using Z minus the number of core electrons
- Explain why Zeff increases across a period but not down a group
- Use Zeff to justify a trend rather than restate it
Lesson
Shielding: inner electrons block the pull
An outer electron is attracted to the nucleus but repelled by every electron between it and the nucleus. The net effect is that the outer electron feels less than the full nuclear charge. Core electrons shield strongly, while electrons in the same shell shield each other only weakly.
Same-shell electrons are at roughly the same distance, so they are poor shields for one another.
Effective nuclear charge
Zeff = Z - S, where Z is the number of protons and S is the shielding constant. A quick classroom estimate takes S as the number of core electrons, so sodium has Zeff approximately 11 - 10 = 1, while chlorine has 17 - 10 = 7.
Zeff = Z - S
Across a period: Zeff climbs
Moving left to right, each step adds one proton and one electron, but the new electron enters the same shell and shields poorly. Z rises while S stays nearly constant, so Zeff climbs sharply. From Na to Cl the estimate goes from 1 to 7, a large increase.
This single fact explains why radius shrinks and ionization energy and electronegativity rise across a period.
Down a group: distance wins
Going down, each step adds a full new shell of core electrons, so S grows almost as fast as Z. Zeff stays roughly constant, around 1 for every alkali metal. What changes is the distance: valence electrons sit in a higher shell, far from the nucleus, and are held loosely.
Use Z − core electrons as a trend model
The estimate Zeff ≈ Z − (core electron count) is a quick model, not an exact experimental value. Electrons in the same shell still repel and shield one another, and orbital penetration affects how strongly an electron samples the nucleus. A 3s electron can reach closer to the nucleus than a 3p electron, so two electrons with the same n need not feel identical attraction. The model is most useful for a comparison: Na and Mg both have a [Ne] core, but Mg has one more proton, so its valence electrons generally feel a stronger pull. State the shared shell and the shielding assumption when using it.
Compare atoms while holding a shell constant
Across a period, added protons increase the pull on valence electrons, while added electrons enter roughly the same principal shell and do little to shield one another. Down a group, a new occupied shell places valence electrons farther from the nucleus and adds inner-electron shielding. Say which comparison you are making before deciding which effect dominates.
Across: stronger nuclear pull in the same shell. Down: distance and shielding rise.
Key ideas
Definition
Shielding
Repulsion from inner electrons that reduces the nuclear attraction felt by an outer electron.
Definition
Effective nuclear charge
The net positive charge experienced by a specified electron, Zeff = Z - S.
Rule
Period behaviour
Across a period Z increases and S is nearly constant, so Zeff increases.
Rule
Group behaviour
Down a group both Z and S increase, so Zeff is roughly constant while distance increases.
Equation
Effective nuclear charge
Zeff = Z - S
- Zeff = net nuclear charge felt by a valence electron
- Z = atomic number, the number of protons
- S = shielding constant, estimated as the number of core electrons
Worked examples
Worked example 2
Explain, using Zeff, why first ionization energy decreases from Li to Cs.
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Worked example 3
Use the core-electron estimate to compare a valence electron in Na (Z = 11) and Mg (Z = 12). What does this predict about their atomic radii?
Try it first: Both atoms have ten neon-core electrons and outer electrons in n = 3.
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Worked example 4
Why is phosphorus generally smaller than silicon despite both using the third valence shell?
Try it first: Compare proton counts and inner-shell shielding.
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Common mistakes
Saying atoms get smaller across a period because electrons are added.
Why it's wrong: Adding electrons alone would enlarge the atom. The shrinking comes from the added protons raising Zeff on a shell that does not change.
Check instead: Attribute the trend to increasing Zeff at constant principal quantum number.
Claiming Zeff increases sharply down a group.
Why it's wrong: Each new period adds core electrons that shield nearly one-for-one, so Zeff is close to constant.
Check instead: Explain group trends with shell distance and shielding, not with a large Zeff change.
Treating shielding by same-shell electrons as complete.
Why it's wrong: Electrons at the same distance screen each other poorly, which is why Zeff climbs across a period at all.
Check instead: Count only core electrons in the quick S estimate.
After the lesson · Question bank
Independent practice
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What you should now know
Effective nuclear charge is the nuclear charge an outer electron actually feels after inner electrons shield it. Zeff rises sharply across a period and barely changes down a group, which is why radius, ionization energy and electronegativity behave as they do.
- Zeff = Z - S captures the pull an outer electron actually feels
- Core electrons shield well, same-shell electrons shield poorly
- Zeff climbs strongly across a period
- Down a group Zeff is nearly constant and distance dominates
Sources and further reading
- Chemistry 2e, Section 6.5: Periodic Variations in Element PropertiesFlowers, Theopold, Langley, Robinson · OpenStax, Rice University · Chapter 6.5View source
Access for free at openstax.org License