Calculadora de Carga Nuclear Efetiva
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
Z_ef = Z − S
About this calculator
The Effective Nuclear Charge Calculator uses Slater's rules to estimate the effective nuclear charge (Z_ef) experienced by an electron in a multielectron atom. The calculation subtracts the shielding constant (S) from the atomic number (Z): Z_ef = Z − S. The constant S is determined based on the electron configuration and the group of the electron of interest, considering contributions from other electrons that shield the nuclear attraction.
This tool is useful for students and chemistry professionals who need to understand periodic properties such as atomic radius, ionization energy, and electronegativity. For example, when comparing elements in the same period, effective nuclear charge helps explain why atomic radius decreases from left to right. It is also applied in disciplines like inorganic chemistry and atomic physics to predict electron behavior in orbitals.
To use the calculator, enter the atomic number of the element and select the electron of interest (e.g., electron in 2p or 3d orbital). The system automatically applies Slater's rules to compute S and displays Z_ef. It is important to remember that Slater's rules are approximations and may not be accurate for all elements, especially those with many electrons or complex configurations.
Cautions: Slater's rules were developed to provide approximate values and do not replace more rigorous quantum calculations. Additionally, shielding varies by orbital; inner electrons shield more than outer ones. The calculator assumes the atom in its ground state and standard electron configuration. For ions or excited states, results may differ.
Frequently asked questions
What is effective nuclear charge?
It is the net nuclear charge felt by an electron, considering shielding by other electrons. It is calculated as Z_ef = Z − S, where Z is the atomic number and S is the shielding constant.
How do Slater's rules determine the shielding constant?
The rules group electrons by shells and subshells. Electrons in the same group as the electron of interest contribute 0.35 each (except 1s, which contributes 0.30), electrons in inner shells contribute larger values, and electrons in outer shells do not contribute.
Does this calculator work for ions?
It is designed for neutral atoms in the ground state. For ions, the electron configuration changes, altering shielding. You can manually adjust the configuration, but results will be approximate.
Why does effective nuclear charge increase from left to right across the periodic table?
Across a period, atomic number increases, but electrons are added to the same shell, increasing shielding only slightly. Thus, Z_ef increases, pulling electrons inward and decreasing atomic radius.
Are Slater's rules accurate for all elements?
No. They are empirical approximations that work well for light and medium elements but may fail for heavy elements or configurations with d and f orbitals. For precise calculations, methods like Hartree-Fock are recommended.