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.