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Effective Nuclear Charge Calculator

Effective Nuclear Charge Calculator

Calculate effective nuclear charge using Slater's rules for electron shielding

Calculate Effective Nuclear Charge

Choose an element from the periodic table

Choose an orbital for the target electron

Carbon Electron Configuration

1s² 2s² 2p²

Effective Nuclear Charge Results

Select an element and orbital to calculate effective nuclear charge.
Choose an element and orbital from the dropdowns

Slater's Rules Summary

Same orbital: 0.35 (or 0.30 for 1s)
Same n, different l: 0.35
n-1 shell (s,p orbitals): 0.85
Inner shells (n-2 and below): 1.00
Formula: Zeff = Z - σ

Example: Carbon 2p Electron

Given Information

Element: Carbon (C, Z = 6)

Electron configuration: 1s² 2s² 2p²

Target orbital: 2p

Target electron: One of the 2p electrons

Applying Slater's Rules

1. Same orbital (2p): 1 other electron × 0.35 = 0.35

2. Same n (2s): 2 electrons × 0.35 = 0.70

3. Inner shell (1s): 2 electrons × 0.85 = 1.70

Total shielding (σ): 0.35 + 0.70 + 1.70 = 2.75

Zeff = 6 - 2.75 = 3.25

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Slater's Shielding Factors

Same orbital
0.35 (0.30 for 1s)
Other electrons in same orbital
Same n, different l
0.35
Same shell, different subshell
n-1 shell (s,p)
0.85
Previous shell s,p electrons
Inner shells
1.00
n-2 and below

Quantum Numbers

n (principal):1, 2, 3, 4...
l (azimuthal):0, 1, 2, 3...

l = 0: s orbital

l = 1: p orbital

l = 2: d orbital

l = 3: f orbital

Periodic Trends

Zeff increases across periods (left to right)

Zeff decreases down groups

Higher Zeff = smaller atomic radius

Higher Zeff = higher ionization energy

Understanding Effective Nuclear Charge

What is Effective Nuclear Charge?

Effective nuclear charge (Zeff) is the net positive charge experienced by an electron in an atom. It's less than the actual nuclear charge because other electrons "shield" the target electron from the full nuclear attraction.

Key Concepts:

  • Nuclear Charge (Z): Total positive charge of nucleus
  • Shielding (σ): Reduction in nuclear attraction due to other electrons
  • Formula: Zeff = Z - σ
  • Units: Elementary charge units

Slater's Rules

Electron Groups

Group electrons by (n,l): (1s), (2s,2p), (3s,3p), (3d), (4s,4p), (4d), (4f), etc.

Shielding Rules

Each electron contributes to shielding based on its orbital type and principal quantum number.

Calculate Zeff

Sum all shielding contributions and subtract from nuclear charge.

Applications and Importance

Atomic Properties

Predicts atomic radius, ionization energy, and electron affinity trends.

Chemical Bonding

Helps understand bond formation and molecular geometry.

Periodic Trends

Explains periodic table patterns and element behavior.

Step-by-Step Calculation Process

1. Write Electron Configuration

Determine the complete electron configuration of the element

Example: Carbon = 1s² 2s² 2p²

2. Choose Target Electron

Select the orbital containing the electron of interest

Example: 2p electron in carbon

3. Apply Slater's Rules

Calculate shielding contribution from each electron group

Example: σ = 1×0.35 + 2×0.35 + 2×0.85 = 2.75

4. Calculate Zeff

Subtract total shielding from nuclear charge

Example: Zeff = 6 - 2.75 = 3.25

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