Classification of Elements and Periodicity

Historical Development:

Mendeleev's Periodic Law: Properties of elements are periodic function of their atomic masses.

Modern Periodic Law (Moseley): Properties of elements are periodic function of their atomic numbers.

Mendeleev's Achievements:

• Predicted properties of undiscovered elements (eka-Al = Ga; eka-Si = Ge; eka-B = Sc)
• Arranged elements based on similarities

Mendeleev's Defects:

• Position of hydrogen ambiguous
• Anomalous pairs: Ar before K, Co before Ni, Te before I (mass order violated)
• Isotopes had no separate place
• Did not explain lanthanide/actinide series

Modern Periodic Table:

• $18$ groups (vertical columns)
• $7$ periods (horizontal rows)
• $4$ blocks: $s, p, d, f$
• Total elements known up to $Z = 118$ (Oganesson, Og)

IUPAC Naming for $Z > 100$:

Suffix '-ium'. Example: $Z = 119$ = unununium (Uue); $Z = 120$ = unbinilium (Ubn).

Period number = principal quantum number ($n$) of outermost shell.

Periods and Number of Elements:

Blocks (based on subshell of last electron entering):

Group Determination:

• For $s$-block: group = number of valence electrons (1 or 2)
• For $p$-block: group = $10 + $ number of valence electrons (13 to 18)
• For $d$-block: group = number of $(n-1)d + ns$ electrons (3 to 12)

Examples:

• Na ($Z = 11$): $[Ne]\,3s^1$ → period 3, group 1, s-block
• Cl ($Z = 17$): $[Ne]\,3s^2\,3p^5$ → period 3, group 17, p-block
• Fe ($Z = 26$): $[Ar]\,3d^6\,4s^2$ → period 4, group 8, d-block
• Ce ($Z = 58$): $[Xe]\,4f^1\,5d^1\,6s^2$ → period 6, f-block (lanthanide)

Metals, Non-metals, and Metalloids:

• Metals: Left and centre — about $78\%$ of elements
• Non-metals: Right (p-block top), e.g., H, C, N, O, halogens, noble gases
• Metalloids: B, Si, Ge, As, Sb, Te, Po (diagonal line)

Effective Nuclear Charge ($Z_{\text{eff}}$): $$Z_{\text{eff}} = Z - \sigma$$ where $\sigma$ = screening (shielding) constant calculated by Slater's rules.

Slater's Rules (for $\sigma$ on a given electron):

• Other electrons in same group (or higher): $0$
• Each other electron in same $(ns, np)$ group: $0.35$ (but $1s$: $0.30$)
• Each electron in $(n-1)$ shell: $0.85$
• Each electron in $(n-2)$ or deeper: $1.00$
• For $d, f$ electrons: each electron in same group $0.35$; all underlying $= 1.00$

Atomic Radius: Half the distance between two bonded atoms.

• Covalent radius (for non-metals): half of bond length in covalent molecule
• Metallic radius (for metals): half the distance between two adjacent metal atoms in crystal
• van der Waals radius: half the distance between two non-bonded atoms

Trends:

• Down a group: Atomic radius increases (new shell added)
• Across a period (L→R): Atomic radius decreases ($Z_{\text{eff}}$ increases for same shell)

Ionic Radius:

• Cations are smaller than parent atoms (loss of outer shell, reduced repulsions)
• Anions are larger than parent atoms (added electrons, more repulsion)
• For isoelectronic species (same e⁻): radius decreases as $Z$ increases. e.g., O²⁻ > F⁻ > Na⁺ > Mg²⁺ > Al³⁺

Ionization Enthalpy ($\Delta_i H$): Minimum energy to remove an electron from an isolated gaseous atom. $$M(g) \to M^+(g) + e^-; \quad \Delta_i H_1 > 0$$

Trends:

• Across period: Increases (smaller atom, more $Z_{\text{eff}}$)
• Down group: Decreases (larger atom)

Successive IEs: $\Delta_i H_1 < \Delta_i H_2 < \Delta_i H_3 < \ldots$

Big jump occurs when noble gas configuration is reached.

Anomalies in IE:

• B < Be (filled $2s^2$ extra stable; removing from $2p^1$ easier than $2s^2$)
• O < N ($2p^3$ half-filled extra stable; removing from $2p^4$ easier than $2p^3$)
• Similar: Al < Mg; S < P

Electron Gain Enthalpy ($\Delta_{eg} H$): Enthalpy change when an electron is added to a neutral gaseous atom. $$X(g) + e^- \to X^-(g); \quad \Delta_{eg}H$$

Trends:

• Across period: Becomes more negative (electron readily accepted by smaller, more electronegative atoms)
• Down group: Less negative (atom larger; added electron experiences less attraction)

Highest electron affinity: Cl (more than F because F is small → electron-electron repulsion in compact $2p$ subshell makes F's $\Delta_{eg}H$ less negative than Cl's).

Electronegativity (EN): Tendency of an atom to attract shared electron pair in a covalent bond. Dimensionless.

Pauling scale: F = $4.0$ (highest); Cs (or Fr) = $0.7$ (lowest among non-radioactive). H = $2.1$.

Other scales: Mulliken (avg of IE and EA), Allred-Rochow.

Trends in EN:

• Across period: Increases (smaller atom, higher $Z_{\text{eff}}$)
• Down group: Decreases (larger atom)

Diagonal Relationship: Diagonally adjacent elements (Li-Mg, Be-Al, B-Si) show similar properties because of similar charge density (charge/size ratio).

Anomalous Properties of 2nd Period Elements:

• Small size, high EN, no d-orbitals → limit covalency to 4
• Examples: Li (resembles Mg), Be (resembles Al)

Periodic Trends Summary: