Effective Nuclear Charge Calculator
Zeff by Slater's rules, with the screening broken down.
Work out Effective Nuclear Charge. Zeff by Slater's rules, with the screening broken down. Says where the method stops being reliable.
Count the ns and np electrons at that level, excluding the one you are looking at. Carbon's 2p electron has three: two in 2s and one other in 2p.
Slater's rules approximate screening with fixed coefficients. Computed values differ, typically in the first decimal place.
Effective nuclear charge (Zeff)
3.25
6 protons, minus 2.75 of screening
Slater's rules are a rule of thumb from 1930, not a measurement. They give carbon's 2p electron a Zeff of exactly 3.25; a proper computed value is 3.136. Use them for trends, not for numbers you intend to quote. The trend is the useful part: across a period, each added proton is screened by less than one full unit, so Zeff climbs and atoms shrink from left to right — the opposite of what adding electrons might suggest.
How the Effective Nuclear Charge Calculator works
Enter the atomic number and how many electrons sit in each shell relative to the one you are interested in, and this applies Slater's rules to give the effective nuclear charge and the screening constant. It is a 1930 approximation and the page says so — good for trends, not for quoting.
Also known as: zeff calculator · slater's rules calculator · shielding constant calculator · electron screening calculator
Frequently asked questions
What is effective nuclear charge?
The net positive charge an electron actually experiences, after inner electrons have shielded it from the nucleus. Zeff = Z − S, where S is the screening constant.
What are Slater's rules?
A set of fixed coefficients for estimating screening: electrons in the same shell contribute 0.35 each, those one shell in contribute 0.85, and anything deeper contributes 1.00. The 1s shell uses 0.30 for the other 1s electron.
Why do atoms get smaller across a period?
Because Zeff rises. Each added proton pulls harder, while the added electron goes into the same shell and screens it by only about 0.35. The net pull increases from left to right, so the shell contracts.
How accurate are Slater's rules?
Enough for trends, not for numbers. Carbon's 2p electron gets a Zeff of 3.25 from Slater and 3.136 from a proper computed treatment. Use them to explain why fluorine is smaller than lithium, not to report a value.
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