Classification of Elements and Periodicity in Properties

1. Genesis of Periodic Classification & Modern Periodic Law

• Historical Milestones:
  • Johann Dobereiner (1829): Law of Triads; the atomic weight of the middle element is approximately the arithmetic mean of the other two (e.g., $\text{Li}\ [7], \text{Na}\ [23], \text{K}\ [39]$ and $\text{Cl}\ [35.5], \text{Br}\ [80], \text{I}\ [127]$).
  • John Newlands (1865): Law of Octaves; every eighth element displays similar properties to the first, valid only up to Calcium ($Z=20$).
  • Lothar Meyer (1869): Plotted physical properties (atomic volume, melting point, boiling point) against atomic weight, revealing periodic recurrence.
  • Dmitri Mendeleev (1869): Published the Periodic Law: "The properties of elements are a periodic function of their atomic weights." Mendeleev left gaps for undiscovered elements: Eka-Aluminium (discovered as Gallium) and Eka-Silicon (discovered as Germanium).
• Modern Periodic Law (Henry Moseley, 1913):
  • Moseley examined characteristic X-ray spectra emitted by elements bombarded with high-energy electrons:

    $$\sqrt{\nu} = a(Z - b)$$

  • A plot of $\sqrt{\nu}$ against atomic number ($Z$) yields a straight line, proving that atomic number is a more fundamental property than atomic mass.
  • Modern Periodic Law Statement: "The physical and chemical properties of the elements are periodic functions of their atomic numbers."

2. IUPAC Systematic Nomenclature for Elements ($Z > 100$)

Until official discovery and naming rights are verified by IUPAC, a systematic name is derived directly from the atomic number digits using numerical roots ending with the suffix "-ium".

• High-Yield NEET Examples:
  • $Z = 104$: Un + nil + quad + ium = Unnilquadium (Unq) → Official: Rutherfordium ($\text{Rf}$)
  • $Z = 107$: Un + nil + sept + ium = Unnilseptium (Uns) → Official: Bohrium ($\text{Bh}$)
  • $Z = 114$: Un + un + quad + ium = Ununquadium (Uuq) → Official: Flerovium ($\text{Fl}$)
  • $Z = 119$: Un + un + enn + ium = Ununennium (Uue) → Family: Group 1 Alkali Metal
  • $Z = 120$: Un + bi + nil + ium = Unbinilium (Ubn) → Family: Group 2 Alkaline Earth

3. Electronic Configurations & Classification into s, p, d, f Blocks

The period number corresponds directly to the highest principal quantum number ($n$) of the valence shell.

1. s-Block Elements (Groups 1 & 2):
   • Valence configurations: Group 1 alkali metals ($ns^1$), Group 2 alkaline earth metals ($ns^2$).
   • Highly electropositive, reactive metals with low ionization enthalpies; form predominantly ionic compounds (except $\text{Li}$ and $\text{Be}$, which form covalent compounds).
2. p-Block Elements (Groups 13 to 18):
   • Outer configuration: $ns^2 np^{1-6}$.
   • Combined with s-block elements, they constitute the Representative Elements (Main Group Elements).
   • Non-metallic character increases across each period; metallic character increases down each group.
3. d-Block Elements (Groups 3 to 12 - Transition Elements):
   • Outer configuration: $(n-1)d^{1-10} ns^{0-2}$.
   • Characterized by variable oxidation states, coloured complex ions, paramagnetism, and catalytic activity.
   • $\text{Zn}, \text{Cd}$, and $\text{Hg}$ have completely filled $(n-1)d^{10} ns^2$ configurations and are not typical transition metals.
4. f-Block Elements (Lanthanoids & Actinoids - Inner Transition Elements):
   • Outer configuration: $(n-2)f^{1-14} (n-1)d^{0-1} ns^2$.
   • Lanthanoids: $\text{Ce} (Z=58)$ to $\text{Lu} (Z=71)$; Actinoids: $\text{Th} (Z=90)$ to $\text{Lr} (Z=103)$.
   • Positioned separately at the base of the periodic table to preserve structure and group symmetry.

4. Periodic Trends in Atomic & Ionic Radii

• Covalent Radius: Half the distance between nuclei of two covalently bonded identical non-metal atoms (e.g., in $\text{Cl}_2$, bond distance $= 198\text{ pm} \implies r_{\text{cov}} = 99\text{ pm}$).
• Metallic Radius: Half the internuclear distance between two adjacent metal cores in a metallic crystal lattice (e.g., in $\text{Cu}$, distance $= 256\text{ pm} \implies r_{\text{met}} = 128\text{ pm}$).
• Van der Waals Radius: Half the distance between nuclei of two non-bonded adjacent atoms of neighboring molecules in the solid state; $r_{\text{vdw}} > r_{\text{met}} > r_{\text{cov}}$.

• Ionic Radii Trends:
  • Cations are smaller than their parent atoms ($r_{\text{cation}} < r_{\text{atom}}$) due to loss of valence electrons and increased $Z_{\text{eff}}$ ($\text{Na} = 186\text{ pm}, \text{Na}^+ = 102\text{ pm}$).
  • Anions are larger than their parent atoms ($r_{\text{anion}} > r_{\text{atom}}$) due to increased electron-electron repulsion and lower $Z_{\text{eff}}$ ($\text{F} = 64\text{ pm}, \text{F}^- = 133\text{ pm}$).
• Isoelectronic Species ($10e^-$ Series):

  $$\text{Al}^{3+} (13p) < \text{Mg}^{2+} (12p) < \text{Na}^+ (11p) < \text{F}^- (9p) < \text{O}^{2-} (8p) < \text{N}^{3-} (7p)$$

• Lanthanoid Contraction: Poor shielding by $4f$ electrons results in an identical atomic radius for 2nd and 3rd row transition element pairs: $\text{Zr} (160\text{ pm}) \approx \text{Hf} (159\text{ pm})$, $\text{Nb} \approx \text{Ta}$, $\text{Mo} \approx \text{W}$.

5. Ionization Enthalpy ($IE$) & Electronic Anomalies

Energy required to remove the most loosely bound electron from an isolated gaseous atom in its ground state:

$$\text{X}(g) \longrightarrow \text{X}^+(g) + e^- \quad (\Delta_i H_1 > 0)$$

Successive ionization enthalpies always increase:

$$\Delta_i H_1 < \Delta_i H_2 < \Delta_i H_3$$

6. Electron Gain Enthalpy ($\Delta_{\text{eg}}H$) & Electronegativity ($EN$)

• Electron Gain Enthalpy ($\Delta_{\text{eg}}H$): Enthalpy change accompanying the addition of an electron to an isolated neutral gaseous atom:

  $$\text{X}(g) + e^- \longrightarrow \text{X}^-(g)$$

  • Halogens have large negative $\Delta_{\text{eg}}H$ values (readily achieve stable noble gas configurations).
  • Noble gases have large positive $\Delta_{\text{eg}}H$ values (incoming electron must enter the next higher shell).
  • Group 2 ($\text{Be}, \text{Mg}$) and Group 15 ($\text{N}$) have nearly zero or positive values due to stable $s^2$ and half-filled $p^3$ configurations.

The 2nd vs 3rd Period Anomaly ($\text{Cl} > \text{F}$ & $\text{S} > \text{O}$)

Due to compact size and high electron density in the $n=2$ shell of $\text{F}$ and $\text{O}$, an added electron encounters intense inter-electronic repulsion. In the larger $n=3$ subshells of $\text{Cl}$ and $\text{S}$, the electron occupies a larger spatial volume with less repulsion:

$$\text{Cl}\ (-349) > \text{F}\ (-328) > \text{Br}\ (-325) > \text{I}\ (-295\text{ kJ mol}^{-1})$$

$$\text{S}\ (-200) > \text{Se}\ (-195) > \text{Te}\ (-190) > \text{Po}\ (-174) > \text{O}\ (-141\text{ kJ mol}^{-1})$$

• Electronegativity ($EN$): Qualitative measure of the tendency of an atom in a molecule to attract shared bonding electrons to itself.
  • Measured on the Pauling scale: Fluorine is arbitrarily assigned $4.0$.
  • $EN$ increases across a period (left to right) and decreases down a group (top to bottom):

    $$\text{F}\ (4.0) > \text{O}\ (3.5) > \text{N}\ (3.0) \approx \text{Cl}\ (3.0) > \text{Br}\ (2.8) > \text{C}\ (2.5) \approx \text{S}\ (2.5) > \text{H}\ (2.1)$$

7. Periodic Trends in Chemical Properties & Reactivity

• Periodicity of Valence / Oxidation State:
  • For representative elements, valence is equal to the number of valence electrons (Groups 1 to 4) or equal to $8 - (\text{valence electrons})$ (Groups 5 to 7).
  • Variable oxidation states are characteristic of d-block transition metals and f-block actinoids.
• Anomalous Properties of Second Period Elements ($\text{Li}, \text{Be}, \text{B}, \text{C}, \text{N}, \text{O}, \text{F}$):
  • Small atomic and ionic size, high electronegativity, and high charge-to-radius ratio.
  • Absence of vacant $d$-orbitals restricts maximum covalency strictly to 4.
  • High tendency to form $p_\pi-p_\pi$ multiple bonds to themselves ($\text{C}=\text{C}, \text{C}\equiv\text{C}, \text{N}\equiv\text{N}$) and other second-row atoms ($\text{C}=\text{O}, \text{C}\equiv\text{N}$).
• Periodic Trends in Oxide Nature:
  • Oxides of elements on the far left are strongly basic: $\text{Na}_2\text{O} + \text{H}_2\text{O} \rightarrow 2\text{NaOH}$.
  • Oxides of elements on the far right are strongly acidic: $\text{Cl}_2\text{O}_7 + \text{H}_2\text{O} \rightarrow 2\text{HClO}_4$.
  • Oxides in the center are amphoteric ($\text{Al}_2\text{O}_3, \text{ZnO}, \text{Ga}_2\text{O}_3$) or neutral ($\text{CO}, \text{NO}, \text{N}_2\text{O}$).