Estimate shielding with Slater rules
Effective nuclear charge, Zeff, estimates how strongly the nucleus attracts a selected electron after accounting for shielding by other electrons. The actual nucleus has charge Z, but an electron does not experience that full attraction because electron–electron repulsion and penetration matter. Choose an element and enter an occupied orbital such as 3s, 3p, 3d, or 4f to apply the traditional Slater grouping rules.
The calculator first builds the neutral ground-state electron configuration. It then separates electrons into the same Slater group, the n−1 shell where applicable, and lower groups. Each count receives the published shielding factor for that rule. The visible result includes S and the subtraction Zeff = Z − S, allowing a periodic-trend exercise to be reproduced by hand.
How shielding factors are assigned
For an ns or np electron, other electrons in the same (ns,np) group normally contribute 0.35 each; another 1s electron contributes 0.30. Electrons in the n−1 shell contribute 0.85 each, and those in n−2 or lower shells contribute 1.00. The selected electron is removed from its own same-group count so it does not shield itself.
For an nd or nf electron, other electrons in that same d or f group contribute 0.35, while electrons in groups to the left contribute 1.00. Groups to the right do not shield the selected electron in this method. These are bookkeeping rules, not measured fractions attached permanently to individual electrons. The tool shows each subtotal so the classification can be compared with a textbook convention.
Select an occupied orbital carefully
An orbital label combines principal quantum number and subshell letter. Sodium has ground-state configuration 1s² 2s² 2p⁶ 3s¹, so 3s is occupied and suitable. Entering 3p for neutral sodium is rejected because no ground-state electron occupies that subshell. For transition elements, review the displayed configuration because familiar filling-order shortcuts have measured exceptions.
The current page calculates neutral atoms. It does not remove electrons for an ion or choose between competing electron configurations for an excited state. If a problem asks about Fe²⁺, construct the ion configuration with the course’s removal rule before using a neutral-atom result. Likewise, make sure the requested convention is Slater rules; other screening models use different equations and can return another value.
Interpret and verify Zeff
Zeff should be less than or equal to Z under these positive shielding factors. Moving across a period often increases effective nuclear charge because nuclear charge grows while shielding does not cancel the increase completely. This helps explain broad trends such as decreasing atomic radius across a period, but the numerical estimate is not a direct atomic radius or ionization energy.
To check a result, add the three shielding subtotals and confirm they equal S. Subtract S from the atomic number printed beside the element. For sodium’s 3s electron, eight n−1 electrons and two lower 1s electrons give S = 8.8 and Zeff about 2.2. If the same electron appears in the same-group count, the answer will be too heavily shielded.
Approximation and privacy
Slater rules are an educational approximation developed before modern high-accuracy electronic-structure methods. Electrons are quantum-mechanical distributions rather than little particles in fixed shielding layers. Use the value to learn grouping and periodic trends, not as precision evidence for spectroscopy, materials design, or a chemical safety decision.
The values are calculated in the current browser tab. NexaCurrent does not upload the quantities, formulas, chemical names, element choices, or other information entered here, and no account is needed. Copying is a deliberate action after the answer and working are visible. Refreshing or leaving the page clears the current calculation, so keep a copied result if it is needed for later study.