Calculate the effective nuclear charge (Zₑfբ) acting on valence electrons using Z and the shielding constant S.
Atomic Parameters
Calculation Results
Enter atomic number and shielding constant to calculate Zₑfբ
About this calculator
Overview
Effective nuclear charge (Zₑfբ) is the net positive charge experienced by an electron in a multi-electron atom. It is less than the actual nuclear charge due to the shielding effect of inner-shell electrons.
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Pro Tips
Z is the total number of protons in the nucleus.
S represents the 'blocking' effect of other electrons between the nucleus and the electron of interest.
The simple formula is Zₑfբ = Z - S.
For more accuracy, use Slater's Rules to calculate S based on electron configuration.
Core electrons (n-1 and lower shells) provide nearly complete shielding (S ≈ 1).
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Fun Facts
"Zₑfբ increases across a period because the number of protons increases while shielding from core electrons remains constant."
"Zₑfբ is responsible for periodic trends like atomic radius, ionization energy, and electronegativity."
"Slater's Rules provide a semi-empirical method for estimating the shielding constant S."
"For hydrogen (Z=1), Zₑfբ = 1 since there are no inner electrons to provide shielding."
"Effective nuclear charge explains why atoms get smaller across a period despite adding more electrons."
"The concept of shielding was first introduced by J.J. Thomson in 1904."
"Zₑfբ determines the strength of attraction between the nucleus and valence electrons."
Formula: Zₑfբ = Z - S
Effective Nuclear Charge Trends
Zₑfբ increases across periods due to increasing Z with constant core shielding
