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Module 5-Effective Nuclear Charge Overview

Sep 10, 2025

Overview

This lecture explains the concept of effective nuclear charge, how it is calculated, and demonstrates finding it for specific electrons in atoms using examples.

Effective Nuclear Charge Concept

  • Electrons are attracted to the nucleus but also repelled by other electrons.
  • Effective nuclear charge (Z_eff) is the average nuclear charge felt by an electron, accounting for inner electron shielding.
  • The formula for effective nuclear charge is Z_eff = Z - S, where Z is the number of protons and S is the number of inner shell electrons.

Step-by-Step Calculation Examples

Sulfur Example (N = 3 Shell)

  • Sulfur (S) has atomic number 16, so Z = 16.
  • A neutral sulfur atom has 16 electrons.
  • Shell configuration: N=1 holds 2 electrons, N=2 holds 8 electrons, and N=3 holds the remaining 6 electrons.
  • Inner shells (N=1 and N=2) contain 10 electrons.
  • Z_eff for an electron in sulfur’s N=3 shell: Z_eff = 16 – 10 = 6.

Chlorine Example (N = 2 Shell)

  • Chlorine (Cl) has atomic number 17, so Z = 17.
  • A neutral chlorine atom has 17 electrons.
  • Electron count: N=1 shell holds 2 electrons, N=2 shell holds 8 electrons, rest are in N=3.
  • For N=2 shell, only N=1 shell electrons are inner (2 electrons).
  • Z_eff for an electron in chlorine’s N=2 shell: Z_eff = 17 – 2 = 15.

Relationships to the Periodic Table

  • For outermost electrons, the effective nuclear charge equals the group number on the periodic table.
  • The same calculation method applies for electrons not in the outermost shell, adjusting the count of inner shell electrons accordingly.

Key Terms & Definitions

  • Effective Nuclear Charge (Z_eff) — The net positive charge felt by an electron after accounting for inner shell electron shielding.
  • Z (Atomic Number) — Number of protons in the nucleus.
  • S (Shielding/Inner Shell Electrons) — Number of electrons in all shells closer to the nucleus than the electron of interest.

Action Items / Next Steps

  • Practice calculating effective nuclear charge for different elements and shells using Z_eff = Z – S.
  • Review group numbers on the periodic table for outer shell electron effective nuclear charge.