Effective Nuclear Charge Calculator

Effective Nuclear Charge Calculator

Estimate Zeff using Z − S; enter atomic number and shielding constant.

2026-05-06T10:07:27.757Z

Effective Nuclear Charge (Zeff)

1.00

Formula: Zeff = Z − S

About Zeff

Effective nuclear charge is a simplified way to estimate the net attraction an electron experiences from the nucleus after accounting for shielding by inner electrons. It helps explain periodic trends such as atomic radius and ionization energy.

How to Use

  1. Enter the atomic number Z.
  2. Enter an estimated shielding constant S (e.g., from Slater\'s rules).
  3. Read Zeff = Z − S and use it to compare relative nuclear attraction across elements.

Worked Example

Given: Z = 11 (Na), S = 8.0
Zeff = 11 − 8 = 3
Result: 3.00

Frequently Asked Questions

What is Zeff?

Effective nuclear charge is the net positive charge felt by an electron after accounting for shielding by other electrons.

How is shielding estimated?

Rules like Slater's provide approximate shielding constants; this tool accepts a user-specified S.

What units is Zeff?

Zeff is a dimensionless effective charge (number).

Why is Zeff useful?

Zeff helps explain trends in atomic radius, ionization energy, and electron affinity across the periodic table.

What if shielding > Z?

A shielding larger than Z yields a negative Zeff — unusual in physical contexts and indicates input review is needed.

Can I use Slater's rules?

Yes — compute S via Slater's method externally and enter the value here.

Is Zeff exact?

Zeff is an approximation; quantum calculations provide more accurate effective potentials.

Any cautions?

Use consistent electron counts and check for typos — Zeff depends on correct inputs.

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