Periodic Trends

1. Atomic Radius

Atomic radius is half the distance between the nuclei of two identical atoms bonded together. Across a period, \(Z_{\text{eff}}\) rises while the shell number stays the same, so the nucleus pulls the electrons closer — radius decreases left → right. Down a group, each new shell sits farther out, so radius increases.

2. Ionic Radius

When an atom loses electrons to form a cation, the remaining electrons are pulled tighter and electron–electron repulsion drops, so the cation is smaller than the neutral atom. When an atom gains electrons to form an anion, added repulsion spreads the electrons out, so the anion is larger. In an isoelectronic series (same number of electrons), the ion with the highest nuclear charge is the smallest — e.g., \(Al^{3+} < Mg^{2+} < Na^+ < F^- < O^{2-}\) for the 10-electron series.

3. Ionization Energy

Ionization energy (IE) is the energy needed to remove one mole of electrons from one mole of gaseous atoms: \(X(g) \to X^+(g) + e^-\). First IE (\(IE1\)) removes the first electron; successive IEs remove later electrons. IE rises left → right (higher \(Z{\text{eff}}\)) and falls down a group (electrons farther from the nucleus, better shielded). Successive IEs always increase, and a huge jump appears when you start removing electrons from a lower, filled shell.

How it works

1. Locate the element on the periodic table.
2. Determine its \(Z_{\text{eff}}\) (topic 17) and its period (shell number).
3. For size: higher \(Z_{\text{eff}}\) (same period) shrinks the atom; more shells (lower in a group) enlarge it.
4. For ions: remove electrons → smaller; add electrons → larger; among isoelectronic ions, more protons → smaller.
5. For IE: higher \(Z_{\text{eff}}\) and smaller radius → harder to remove an electron → higher IE.
6. For electron affinity and metallic character: elements on the right (nonmetals) gain electrons readily; elements on the left and bottom (metals) lose them readily.

Common confusions

Memory aids

"Radius: down the stairs and to the left, atoms get bigger." Imagine walking down a group (bigger) and left across a period (bigger). Ionization energy runs the opposite direction: up and to the right, atoms hold electrons tighter.

Quick review

Topic Recap

All the major periodic trends trace back to two factors: effective nuclear charge and the number of electron shells. Atomic radius and metallic character grow down and to the left; ionization energy and electron affinity grow up and to the right. Cations shrink and anions swell relative to their parent atoms, and successive ionization energies reveal exactly how many electrons an atom can comfortably lose before the next removal becomes prohibitively expensive.

Knowledge Check

1. Does atomic radius increase or decrease as you move from left to right across period 2? Why?
2. Which is larger, \(Cl\) or \(Cl^-\), and why?
3. Arrange \(S^{2-}, Cl^-, K^+, Ca^{2+}\) (all 18 electrons) by increasing radius.
4. Why is \(IE_2\) of sodium much larger than \(IE_1\)?
5. Which has more metallic character, potassium or bromine? Explain.

Answers and Rationales

1. It decreases. Across period 2, \(Z_{\text{eff}}\) rises while electrons stay in the \(n = 2\) shell, so the nucleus pulls them closer.
2. \(Cl^-\) is larger. Adding an electron increases electron–electron repulsion and spreads the cloud out, while the nuclear charge is unchanged.
3. \(Ca^{2+} < K^+ < Cl^- < S^{2-}\). All have 18 electrons; more protons pull harder, so \(Ca^{2+}\) (20 protons) is smallest and \(S^{2-}\) (16 protons) is largest.
4. \(IE_1\) removes sodium's lone \(3s\) valence electron, but \(IE2\) removes a \(2p\) core electron that feels a much higher \(Z{\text{eff}}\) — hence the huge jump.
5. Potassium. It is farther down and to the left, so its valence electron is easier to remove; bromine, a nonmetal near the top right, gains electrons instead.