Effective nuclear charge
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The effective nuclear charge is the net positive charge experienced by an electron in a multielectron atom. The term "effective" is used because the shielding effect of negative electrons prevents higher orbital electrons from experiencing the full nuclear charge.
In an atom with one electron, that electron experiences the full charge of the positive nucleus. In this case, the effective nuclear charge can be calculated from Coulomb's law.
However, in an atom with many electrons, the outer electrons are simultaneously attracted to the positive nucleus and repelled by the negatively charged electrons. The effective nuclear charge on such an electron is given by the following equation:
Zeff = Z - S
Zeff is also often known as "Z* ".
Where Z is the number of protons in the nucleus and S is the average number of electrons between the nucleus and the electron in question.
S can be found by the systematic application of various rule sets, the simplest of which is known as "Slater's rules" (for the scientist Slater).
Trends
Down the Periodic Table (Top to Bottom)
Effective Nuclear Charge generally decreases for elements, going down the Periodic Table. This is because elements have:
- More Protons
- Greater Distance between the nucleus and the electrons
- Greater Shielding of electrons, since there are more electrons
More Protons = Greater Force of electrostatic attraction
More Electrons = More Shielding = Repulsion
Distance = Less force of electrostatic attraction
The increase in repulsion is greater than the increase of electrostatic attraction due to the Protons; Thus Zeff decreases going down the Periodic Table.
Across the Periodic Table (Left to Right)
Effective Nuclear Charge generally increases for elements, going across the Periodic Table. Elements have:
- Slightly More Protons
- Slightly More Electrons
- Same Distance
- Same Shielding since electrons are just added on to the current orbital
The increase in the electrostatic force provided by the protons is greater than the increase in repulsion due to shielding and distance. Therefore, Across the Periodic Table, Effective Nuclear Charge increases.
Resources
- Brown, Theodore; LeMay, H.E.; & Bursten, Bruce (2002). Chemistry: The Central Science (8th revised edition). Upper Saddle River, NJ 07458: Prentice-Hall. ISBN 0-13-061142-5.