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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

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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.

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 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.

    0 of 3 steps revealed.

    Worked example 2

    Explain, using Zeff, why first ionization energy decreases from Li to Cs.

      0 of 3 steps revealed.

      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.

      Practice this skill

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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
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      Sources and further reading

      • Chemistry 2e, Section 6.5: Periodic Variations in Element Properties
        Flowers, Theopold, Langley, Robinson · OpenStax, Rice University · Chapter 6.5
        View source

        Access for free at openstax.org License