What is meant by the term effective nuclear charge, Z_eff, and what causes it?

Verified step by step guidance

1. The effective nuclear charge, denoted as \( Z_{\text{eff}} \), is the net positive charge experienced by an electron in a multi-electron atom.
2. It accounts for the actual nuclear charge (the total positive charge of the nucleus) and the shielding effect caused by other electrons in the atom.
3. The shielding effect occurs because inner electrons partially block the attraction between the nucleus and the outer electrons, reducing the full nuclear charge experienced by the outer electrons.
4. The effective nuclear charge can be estimated using the formula: \( Z_{\text{eff}} = Z - S \), where \( Z \) is the atomic number (total number of protons) and \( S \) is the shielding constant, representing the extent of electron shielding.
5. Understanding \( Z_{\text{eff}} \) is crucial for explaining trends in the periodic table, such as atomic size, ionization energy, and electron affinity, as it influences how strongly electrons are held by the nucleus.

Key Concepts

Effective Nuclear Charge (Z_eff)

Effective nuclear charge (Z_eff) refers to the net positive charge experienced by an electron in a multi-electron atom. It accounts for the actual nuclear charge (the total number of protons) minus the shielding effect caused by other electrons. This concept helps explain trends in atomic size, ionization energy, and electron affinity across the periodic table.

Shielding Effect

The shielding effect occurs when inner-shell electrons partially block the attraction between the nucleus and the outer-shell electrons. This reduction in effective nuclear charge means that outer electrons feel less pull from the nucleus, which influences their energy levels and reactivity. The greater the number of inner electrons, the more significant the shielding effect.

Trends in the Periodic Table

Trends in the periodic table, such as atomic radius, ionization energy, and electronegativity, are influenced by effective nuclear charge. As you move across a period, Z_eff increases due to the addition of protons without a corresponding increase in shielding, leading to smaller atomic radii and higher ionization energies. Conversely, down a group, increased shielding from additional electron shells results in a decrease in Z_eff, leading to larger atomic sizes.