Effective Nuclear Charge Calculator Formula

Understand the math behind the effective nuclear charge calculator. Each variable explained with a worked example.

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Formulas Used

Effective Nuclear Charge (Z_eff)

z_eff = z - sigma

Variables

VariableDescriptionDefault
zAtomic Number (Z)11
sigmaShielding Constant (σ)8.8

How It Works

Effective Nuclear Charge

Formula

Z_eff = Z − σ

Where:

  • Z_eff = effective nuclear charge felt by valence electron
  • Z = atomic number (total protons)
  • σ = shielding constant (from Slater's rules)

    • Inner electrons shield outer electrons from the full nuclear charge. Z_eff increases across a period (more protons, similar shielding) and stays roughly constant down a group.

    Worked Example

    Sodium (Z = 11) with shielding constant σ = 8.8 for the 3s electron.

    z = 11sigma = 8.8
    1. 01Z_eff = Z - σ
    2. 02Z_eff = 11 - 8.8
    3. 03Z_eff = 2.2
    4. 04The 3s electron feels an effective charge of +2.2

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