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Effective nuclear charge calculator

Estimate the nuclear charge experienced by an electron in a chosen occupied subshell using Slater shielding rules.

Calculator

Atomic number
11
Shielding constant S
8.800000
Effective nuclear charge
2.200000
Electron configuration
1s2 2s2 2p6 3s1
Shielding contributions
SubshellOther electronsShielding per electronContribution
1s2.0000001.0000002.000000
2s2.0000000.8500001.700000
2p6.0000000.8500005.100000

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How this calculator works

Choose an electron in an occupied subshell. Group ns and np together. Other electrons in that group shield by 0.35 each, except 1s where the factor is 0.30. For an ns or np electron, electrons in shell n-1 shield by 0.85 and deeper shells by 1. For an nd or nf electron, all electrons in groups to its left shield by 1 and others in its own group by 0.35. Outer groups contribute zero. This empirical estimate is orbital-dependent; heavy configurations above Z = 103 use an Aufbau prediction.

Formula

Z effective = Z - S, where S is the sum of Slater shielding contributions from every other electron.

Worked example

For a sodium 3s electron, S = 8 x 0.85 + 2 x 1 = 8.8, so Z effective = 11 - 8.8 = 2.2. A helium 1s electron has S = 0.30 and Z effective = 1.70.

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Frequently asked questions

Why exclude one electron?

An electron does not shield itself. One is subtracted from its own subshell.

Can I choose an empty orbital?

No. Slater rules here estimate shielding of an occupied electron in the neutral configuration.

Is this an exact charge?

No. It is a useful empirical model, not a direct measurement or a full quantum calculation.

Sources

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