Effective nuclear charge

The effective nuclear charge, also known as the kernel 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.

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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, and 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:

Z_eff = Z − S

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, and

S can be found by the systematic application of various rule sets, the simplest of which is known as "Slater's rules" (after the scientist John C. Slater).

Note: Z_eff is also often known as "Z* ".

A simple way to calculate the effective nuclear charge is to take the total protons minus all electrons excluding the valence electrons.

Trends

Down the Periodic Table (Top to Bottom)

Effective Nuclear Charge for the outermost valence electron slightly increases for elements, going down the Periodic Table. This is because elements have:

• More Protons - More Protons = Greater Force of electrostatic attraction
• Greater Shielding of electrons, since there are more electrons - More Electrons = More Shielding = Greater Repulsion

The increase in repulsion is less than the increase of electrostatic attraction due to the Protons; Thus Z_eff increases going down the Periodic Table. - Note: this is wrong since the ionization energy or electron affinity decreases going down

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 level

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.

These trends can be used to explain other trends between elements. Properties such as atomic radius, Melting and Boiling Points, electronegativity and ionization energy can be discussed using the Effective Nuclear Charge theory.

Generally, as Z_eff increases:

• Atomic Radii decrease (Greater pull on electrons means that they are held on "tighter") but only as you move from the left to the right of the periodic table; atomic radii increase from top to bottom because of added shells (despite the decreasing Z_eff
• Melting and Boiling Points increase (Higher intermolecular forces as a result of high Zeff means that more energy is needed to break intermolecular forces)
• Electronegativity increases (Directly related to Z_eff)
• Ionization energy increases (If Z_eff is the net positive force pulling force experienced by an electron, and the ionization energy is the energy required to remove the outer most electron, the more Z_eff, the more energy required to remove it).

It is important to bear in mind that when speaking about the location of electrons with respect to the nucleus, we are talking about a probability (see Heisenberg's uncertainty principle). The actual effective nuclear charge is therefore in fluctuation due to the location of an electron relative to the nucleus, and also due to electron-electron repulsions. Any theorized effective nuclear charge is a kind of mean between larger and smaller positive charges experienced during the path of an electron.

Related

• Slater's rules
• Slater-type orbitals
• Electronegativity

Resources

• Brown, Theodore; LeMay, H.E.; & Bursten, Bruce (2002). Chemistry: The Central Science (8th revised edition). Upper Saddle River, NJ 07458: Prentice-Hall. ISBN 0-61155-61141-5.