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
Effective Nuclear Charge Results
Slater's Rules Summary
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
Slater's Shielding Factors
Quantum Numbers
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