Effective Nuclear Charge Calculator
Effective Nuclear Charge Calculator
In effective nuclear charge calculator, enter atomic number of element. Select electron shell (1s, 2s, 2p, etc.) for which you want to calculate Zeff. The calculator considers shielding effects from inner electrons and other electrons in the same shell to determine the effective nuclear charge experienced by the electron of interest.
Sodium (Na)
- Z = 11 (Atomic number)
- S = 10 (Shielding constant using Slater’s rules)
Zeff = Z – S = 11 – 10 = 1
Result: The outer electron experiences a net charge of +1.
How to Calculate Effective Nuclear Charge
To accurately calculate effective nuclear charge, Identify the atomic number (Z) of the element. Determine which electron shell you’re calculating for (1s, 2s, 2p, etc.). Calculate shielding constant (S) using Slater’s rules for inner shell and same-shell electrons.
Subtract shielding constant from the atomic number to find the effective nuclear charge (Zeff = Z – S).
Oxygen (O)
- Z = 8 (Atomic number)
- S = 3.45 (Shielding constant)
Zeff = Z – S = 8 – 3.45 = 4.55
Result: The outer electrons experience a net charge of +4.55.Chlorine (Cl)
- Z = 17
- S = 15.85
Zeff = Z – S = 17 – 15.85 = 1.15
Result: The outer electron experiences a net charge of +1.15.
Effective Nuclear Charge Formula
Zeff = Z - S
Where:
Z = Atomic Number
S = Shielding Constant
Slater's Rules for S:
- Inner shell electrons shield 1.00 unit each
- Same shell electrons shield ~0.35 units each
- Outer shell electrons provide no shielding
The formula requires:
- Atomic Number: Element’s nuclear charge
- Electron Configuration: Electronic structure
- Shell Location: Target electron position
- Shielding Rules: Slater’s constants
Lithium (2s electron) Example
- Atomic Number: 3
- Inner Electrons: 2 (1s²)
- Configuration: [He]2s¹
- Calculation: 3 – (2 × 1.00) = 1.00 Zeff
Carbon (2p electron) Example
- Atomic Number: 6
- Inner Electrons: 4 (1s²2s²)
- Configuration: [He]2s²2p²
- Calculation: 6 – (4 × 1.00 + 1 × 0.35) = 1.65 Zeff
Sodium (3s electron) Example
- Atomic Number: 11
- Inner Electrons: 10 (1s²2s²2p⁶)
- Configuration: [Ne]3s¹
- Calculation: 11 – (10 × 1.00) = 1.00 Zeff
Aluminum (3p electron) Example
- Atomic Number: 13
- Inner Electrons: 12 (1s²2s²2p⁶3s²)
- Configuration: [Ne]3s²3p¹
- Calculation: 13 – (10 × 1.00 + 2 × 0.35) = 2.30 Zeff
Chlorine (3p electron) Example
- Atomic Number: 17
- Inner Electrons: 14 (1s²2s²2p⁶3s²3p⁴)
- Configuration: [Ne]3s²3p⁵
- Calculation: 17 – (10 × 1.00 + 6 × 0.35) = 4.90 Zeff
What is Effective Nuclear Charge?
Effective Nuclear Charge (Zeff) represents the net positive charge that an electron experiences in an atom, considering both the full nuclear charge and the shielding effects of other electrons. This concept explains various atomic properties including atomic size, ionization energy, and electron affinity. The effective charge decreases for outer shell electrons due to shielding by inner electrons, while nuclear charge increases across a period, leading to periodic trends in atomic properties.