Effective Charge Calculator

Sum of shielding contributions from other electrons (Slater's rules).
Chemistry

Calculate the effective nuclear charge (Z*) experienced by an electron using Slater's rules.

Formula

Z* = Z − σ
  • Z* = effective nuclear charge (what an electron 'feels' after accounting for shielding).
  • σ = shielding constant (sum of contributions from all other electrons).
  • Slater's rules: same shell electrons contribute 0.35; (n−1) shell contribute 0.85; inner shells contribute 1.00.
  • Example: Na (Z=11) valence electron: σ = 2×1 + 8×0.85 = 8.8; Z* = 11 − 8.8 = 2.2.

Sodium (Na, Z=11) valence electron

Inputs
  • Atomic Number (Z): 11
  • Shielding Constant (σ): 8.8

Z* = 11 − 8.8 = 2.2.

Frequently asked questions

What are Slater's rules?
A set of empirical rules for estimating the shielding constant σ for an electron in an atom.
How does Z* affect atomic radius?
Higher Z* means stronger attraction to the nucleus → smaller atomic radius.