Effective Nuclear Charge Calculator (Z-eff via Slater's Rules)

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Select any element from hydrogen (Z=1) to oganesson (Z=118). The ground-state electron configuration is determined automatically, including Aufbau exceptions.
Choose which orbital's electron you want to analyze. Slater's rules calculate the net nuclear charge that electron experiences after accounting for shielding from all other electrons.
Effective nuclear charge (Z-eff)Moderately shielded
4.55

Net positive charge felt by the target electron after shielding

Shielding constant (sigma)3.45
Atomic number (Z)8
Target orbital2p
ElementOxygen (O)
Electron configuration1s2 2s2 2p4
4.55
Heavy shielding<2Moderate shielding2-8Light shielding8-18Very low shielding18+

Z-eff = 4.55 for the 2p electron in Oxygen (O).

  • The 2p electron in Oxygen (O) experiences a Z-eff of 4.55, meaning it is attracted toward a net nuclear charge of +4.55 rather than the full +8.
  • Inner and same-shell electrons provide a total shielding constant of 3.45, reducing the bare nuclear charge by 43.1%.
  • Across period 2 and 3, Z-eff increases steadily from left to right because each added proton outweighs the additional shielding from a same-shell electron (which contributes only 0.35 per electron).

Next stepCompare Z-eff values across the same period to see why atomic radius shrinks and ionization energy rises from left to right on the periodic table.

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