# 1.2: Periodic Trends and their Relationships

A note from Dr. Haas: By now, you should be able to describe Shielding, Penetration, and $$Z_{eff}$$, and you should be able to predict the $$Z_{eff}$$ of a given electron in any atom or ion using Slater's rules. And, you should be able to explain how shielding and penetration result in observed trends in $$Z_{eff}$$ across the periodic table.

Shielding and penetration are responsible not only for trends in $$Z_{eff}$$, but also for trends in atomic/ionic size, ionization energy, electron affinity, and electronegativity. This responsibility is primarily due to the relationship between $$Z_{eff}$$ and these other properties. Go back to the Review on Periodic Trends sections and re-read that material now that you know more about $$Z_{eff}$$ (or Z*), shielding, and penetration.

## Introduction

This page will explicitly describe the relationship between $$Z_{eff}$$, atomic/ionic size, and ionization energy. Ionization energy, and electron affinity follow similar trends, so, we'll focus on the relationship between $$Z_{eff}$$ and ionization energy (further discussion of electron affinity and electronegativity are somewhat redundant once you understand ionization energy).

In the page on $$Z_{eff}$$ you learned that $$Z_{eff}$$ modulates the attractive force between electrons and the nucleus. The larger the $$Z_{eff}$$, the stronger (more negative) the attractive force between the nucleus and any electrons becomes. The attractive force between valence electrons and the nucleus defines an atom or ion's size and its ionization energy. Since these trends are correlated to $$Z_{eff}$$, they are also dependent on, and explained by, the combined phenomena of shielding and penetration.

## $$Z_{eff}$$ is inversely related to atomic size

When the attractive force is strong, the nucleus pulls electrons closer to itself, resulting in a smaller atomic/ionic size. On the other hand, a weaker attractive force is not as effective at retaining the electrons and results in larger atomic/ionic radius.

The relationships between $$Z_{eff}$$ and size are summarized as follows:

• Larger valence $$Z_{eff}$$ = smaller atomic/ionic size
• Smaller valence $$Z_{eff}$$ = larger atomic/ionic size

## $$Z_{eff}$$ is directly related to ionization energy

When the attractive force between the nucleus and valence electrons is large, more energy is required to remove (ionize) the outermost electron. Thus, the following relationships exist between $$Z_{eff}$$ and ionization energy:

• Larger valence $$Z_{eff}$$ = larger ionization energy (harder, or requires more energy, to remove the electron)
• Smaller valence $$Z_{eff}$$ = smaller ionization energy (easier, or requires less energy, to remove the valence electron)

## Ionization energy is inversely related to atomic size

Since both ionization energy and atomic size are related to $$Z_{eff}$$, we can predict trends in ionization energy from atomic size and vice versa.

The closer an electron is to the nucleus, the stronger the attractive force will be (from Coulomb's Law). And the stronger the attractive force, the more difficult it will be to remove the outermost electron. The following relationships are true:

• Smaller atomic size = larger ionization energy (harder, or requires more energy, to remove the electron)
• Larger atomic size = smaller ionization energy (easier, or requires less energy, to remove the valence electron)

Modified or created by Kathryn Haas (khaaslab.com)