Effective Nuclear Charge Calculator

About Effective Nuclear Charge

The effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the shielding effect of inner-shell electrons that reduce the attraction between the nucleus and the outer electrons.

Uses of Effective Nuclear Charge:

• Understanding atomic radii trends across the periodic table
• Explaining ionization energy variations
• Analyzing electron affinity patterns
• Predicting chemical reactivity of elements
• Understanding periodic trends in electronegativity

How to Use This Calculator:

1. Enter the atomic number (Z) of the element (number of protons)
2. Enter the shielding constant (σ) for the electron in question
3. Click "Calculate Effective Nuclear Charge"
4. The result will display the effective nuclear charge (Z_eff)

Determining Shielding Constants:

The shielding constant depends on the electron configuration. Some common rules:

• Electrons in higher shells (n) shield very little (σ ≈ 0)
• Electrons in the same group (n) shield by 0.35 each (except 1s, which shields by 0.30)
• Electrons in n-1 shells shield by 0.85 each
• Electrons in n-2 or lower shells shield by 1.00 each

Example Calculation for Sodium (Na):

For the 3s electron in sodium (Z=11, electron configuration: 1s²2s²2p⁶3s¹):

Shielding from 1s electrons: 2 × 0.85 = 1.70

Shielding from 2s and 2p electrons: 8 × 0.85 = 6.80

Total shielding constant (σ) = 1.70 + 6.80 = 8.50

Effective nuclear charge: Z_eff = 11 - 8.50 = 2.50