Classification of Elements & Periodicity

The modern periodic law, proposed by Henry Moseley in 1913, states that the physical and chemical properties of elements are periodic functions of their atomic numbers (not atomic masses, as Mendeleev originally suggested). The long form of the periodic table contains 7 periods (horizontal rows) and 18 groups (vertical columns), organized into four blocks based on the subshell being filled: s-block (Groups 1-2, outer configuration $ns^{1}$-2), p-block (Groups 13-18, $ns^{2} \; np^{1}$-6), d-block (Groups 3-12, (n-1)$d^{1}$-10 $ns^{0}$-2), and f-block (lanthanoids and actinoids, (n-2)$f^{1}$-14).

Atomic radii decrease across a period due to increasing effective nuclear charge (Zeff) at constant principal quantum number, and increase down a group as new electron shells are added. Ionic radii follow a related pattern: cations are smaller than their parent atoms (loss of outermost electrons increases Zeff per electron), while anions are larger (additional electrons increase repulsion). In isoelectronic species (same number of electrons), the radius decreases with increasing nuclear charge. For the 10-electron series: $N^{3}$- (146 pm) > $O^{2}$- (140 pm) > F^- (133 pm) > Na⁺ (98 pm) > $Mg^{2}$+ (66 pm) > $Al^{3}$+ (51 pm).

Ionization enthalpy (IE) generally increases across a period and decreases down a group. Two critical exceptions in the second period arise: IE of Be (899 kJ/mol) is greater than that of B (800 kJ/mol) because Be loses a 2s electron (fully filled, stable) while B loses a 2p electron (easier to remove). Similarly, IE of N (1402 kJ/mol) exceeds that of O (1314 kJ/mol) because nitrogen has a half-filled $2p^{3}$ configuration, which has extra stability.

Electron gain enthalpy (EGE) becomes more negative across a period and less negative down a group. Notably, chlorine (not fluorine) has the most negative EGE (-349 kJ/mol vs -328 kJ/mol for F) because fluorine's tiny 2p orbitals create strong electron-electron repulsion. Noble gases have positive EGE (complete octet), and Groups 2 and 15 show less negative or positive values due to filled/half-filled subshell stability.

Electronegativity on the Pauling scale increases across a period and decreases down a group, with fluorine being the most electronegative element (4.0). The electronegativity difference between bonded atoms determines bond polarity.

Diagonal relationships occur between Li-Mg, Be-Al, and B-Si, where elements show similar properties due to comparable charge-to-size ratios. For example, both Li and Mg form normal oxides (Li₂O, MgO), their carbonates decompose on heating, and their hydroxides are weak bases.

The key testable concept is the exceptions to periodic trends: IE(Be) > IE(B) due to 2s vs 2p removal, IE(N) > IE(O) due to half-filled $2p^{3}$ stability, and EGE(Cl) > EGE(F) due to small size of fluorine causing electron repulsion.