Topic 1.7 Periodic Trends: explain and predict the trends in atomic and ionic radius, ionization energy, and electronegativity using effective nuclear charge and shielding.

What this topic is asking

The College Board (Topic 1.7) wants you to explain and predict periodic trends: atomic and ionic radius, ionization energy, and electronegativity. Crucially, you must justify each trend using two underlying ideas, effective nuclear charge and shielding, not merely state the direction of the arrow.

The driving idea: effective nuclear charge

Every trend in this topic comes back to $Z_{eff}$ and Coulomb's law: the more strongly the nucleus pulls on the outer electrons, the smaller the atom and the harder its electrons are to remove. Two changes alter that pull as you move around the table: adding protons (raises $Z_{eff}$) and adding shells (increases distance and shielding, lowering $Z_{eff}$ felt by the valence electrons).

Atomic radius

So the smallest atoms are at the top right (helium, fluorine) and the largest at the bottom left (caesium, francium).

Ionization energy

The first ionization energy is the energy needed to remove the most loosely held electron from a gaseous atom. It mirrors how tightly the valence electrons are held:

• Increases across a period as $Z_{eff}$ rises and the radius shrinks.
• Decreases down a group as the valence electron sits farther out and is better shielded.

There are two small but examinable dips. Removing an electron from a higher-energy $p$ subshell (for example boron versus beryllium) takes slightly less energy than from a full $s$ subshell, and removing an electron that breaks up a paired set (oxygen versus nitrogen) is slightly easier because pairing adds repulsion. Successive ionization energies always rise, and a large jump appears when you start removing core electrons; that jump reveals how many valence electrons an element has.

Electronegativity

Electronegativity measures how strongly an atom attracts the shared electrons in a bond. It follows the same logic as ionization energy: it increases across a period and decreases down a group, so fluorine (top right, excluding the noble gases) is the most electronegative element. Electronegativity differences predict bond polarity (Topic 2.1).

Ionic radius

Forming ions changes size predictably. A cation is smaller than its parent atom because it has lost its outermost shell (or at least lost electrons, raising $Z_{eff}$ per electron). An anion is larger because added electrons increase electron-electron repulsion while the nuclear charge is unchanged. For isoelectronic species (same number of electrons), the one with more protons is smaller, because the same electron cloud is pulled in by a greater charge. Tying these together, the whole topic is one idea applied repeatedly: balance the nuclear pull against distance and shielding, and every ranking follows. When a question asks you to "explain", name $Z_{eff}$ and shielding explicitly, because the College Board scores the reasoning, not just the correct order.

Try this

Q1. Rank Cl, Br, and I by electronegativity, highest first, and justify. [2 points]

• Cue. Cl $>$ Br $>$ I; electronegativity decreases down group 17 as the valence electrons get farther from the nucleus and more shielded.

Q2. Explain why a magnesium cation, $\text{Mg}^{2+}$, is smaller than a neutral magnesium atom. [1 point]

• Cue. $\text{Mg}^{2+}$ has lost its $3s$ electrons, removing the outermost shell, and the remaining electrons feel a greater $Z_{eff}$ per electron, so the ion is smaller.