Organization of the Periodic Table

The modern periodic table arranges elements in order of increasing atomic number ($Z$, the number of protons). Elements are organized into periods (horizontal rows, numbered 1-7) and groups (vertical columns, numbered 1-18). Elements in the same group share similar valence electron configurations and therefore similar chemical properties — this is the basis of the periodic law: properties of elements are periodic functions of their atomic number.

The table is divided into blocks based on which subshell the last electron enters: s-block (groups 1-2), p-block (groups 13-18), d-block (transition metals, groups 3-12), and f-block (lanthanides and actinides, placed below the main table).

Atomic and Ionic Radius

Atomic radius decreases across a period (left to right) because the nuclear charge increases while electrons are added to the same principal shell, pulling the electron cloud in tighter. Atomic radius increases down a group because each successive element adds a new principal quantum shell, which outweighs the increase in nuclear charge.

Worked example: Na (radius $\approx 186\text{ pm}$) is larger than Mg ($\approx 160\text{ pm}$) because both are in Period 3, but Mg has one more proton pulling the same-shell electrons in more tightly. K ($\approx 227\text{ pm}$) is larger than Na because K's valence electron is in shell $n=4$ versus for Na.

Cations are always smaller than their parent atom (electrons removed, often losing a whole shell); anions are always larger than their parent atom (added electrons increase electron-electron repulsion). So $Na^+ < Na$ and $Cl^- > Cl$.

Ionization Energy

Ionization energy ($IE$) is the energy required to remove an electron from a gaseous atom or ion: $X(g) \rightarrow X^+(g) + e^-$. First ionization energy generally increases across a period (harder to remove an electron as nuclear charge increases and radius shrinks) and decreases down a group (outer electron is farther from the nucleus and shielded by more inner shells).

There are notable exceptions: $IE$ drops slightly from Group 2 to Group 13 (e.g. Be to B) because the p-orbital electron being removed is higher in energy and better shielded than the filled s-orbital. It also drops from Group 15 to Group 16 (e.g. N to O) because removing an electron from O relieves electron-pairing repulsion in a half-filled p-subshell, making it easier than the trend predicts.

Worked example: ranking Mg, Al, and Na by first $IE$: Na (496 kJ/mol) < Al (577 kJ/mol) < Mg (738 kJ/mol) — Mg's filled 3s² subshell is unusually stable, giving it a higher $IE$ than Al despite Al having a higher atomic number.

Electron Affinity and Electronegativity

Electron affinity is the energy change when a gaseous atom gains an electron: $X(g) + e^- \rightarrow X^-(g)$. Most electron affinities are exothermic (energy released) and become more negative (more favorable) across a period, with halogens showing the most negative values because they need just one electron to achieve a noble gas configuration.

Electronegativity is the tendency of an atom to attract shared electrons in a covalent bond, measured on the Pauling scale. It increases across a period and decreases down a group, following the same underlying logic as ionization energy. Fluorine is the most electronegative element ($\chi = 3.98$); francium and cesium are the least ($\chi \approx 0.7$).

Metallic and Non-Metallic Character

Metallic character (tendency to lose electrons and form cations) increases down a group and decreases across a period — it is essentially the inverse trend of ionization energy and electronegativity. This is why metals cluster on the left and bottom-left of the periodic table, non-metals on the upper right, and metalloids (B, Si, Ge, As, Sb, Te) form a diagonal staircase boundary between them, showing intermediate properties.

Why This Matters for Your Exams

Almost every periodicity question is really the same question asked six ways: does this property increase or decrease across a period, and does it increase or decrease down a group? If you memorize the reason (nuclear charge vs. shielding vs. added shells) rather than just the direction, you can correctly predict the answer even for elements you've never explicitly compared, and you can explain the exceptions (Be/B, N/O) instead of just memorizing them as anomalies.