Electronic Structure and Configuration of Elements – Key Vocabulary

Introduction to Atomic Structure

• Electronic structure = arrangement of electrons around the nucleus.
  • Dictates chemical reactivity, placement in the periodic table, physical/chemical properties.
• Progress in atomic theory shows a shift from tangible particles to probabilistic wave-mechanics.

Historical Development of Atomic Models

Dalton’s Atomic Theory (1803)

• First scientific model based on experiments.
• Postulates
  • Atoms are indivisible, indestructible particles.
  • All atoms of one element are identical in mass & properties.
  • Atoms are conserved in chemical reactions; only rearranged.
  • Compounds form when atoms combine in simple, whole-number ratios.
• Limitations
  • No sub-atomic particles → cannot explain electrons, protons, neutrons.
  • Fails to account for isotopes (atoms of same element with different masses).

Thomson’s “Plum-Pudding” Model (1897)

• Discovery: electron (via cathode-ray tubes).
• Model features
  • Atom = diffuse sphere of positive charge with embedded electrons (“plums in a pudding”).
  • Overall electrically neutral.
• Limitation: Could not explain scattering results later observed by Rutherford.

Rutherford’s Nuclear Model (1911)

• Gold-foil (α-particle) experiment.
  • Most α passed through → atom mostly empty space.
  • Some deflected → small, dense, positive centre (nucleus).
  • Few bounced back sharply → nucleus contains most mass.
• Model: electrons orbit a central nucleus.
• Limitations
  • Could not explain why orbiting e⁻ do not spiral into nucleus (instability).
  • Failed to explain discrete line spectra.

Bohr’s Planetary Model (1913)

• Incorporated early quantum ideas to explain H spectrum.
• Postulates
  • Electrons move in fixed, quantised circular orbits (energy levels). No radiation while in a permitted orbit.
  • Absorb/emit energy only when jumping between levels → explains line spectra.
• Hydrogen energy formula
  E_n = -\frac{13.6\,\text{eV}}{n^2}
• Limitations
  • Accurate only for one-electron systems (H, He⁺, Li²⁺).
  • No sub-level (s, p, d, f) splitting, fine structure, chemical bonding.

Quantum-Mechanical Model (1926 → present)

• Key contributors: Schrödinger (wave equation), Heisenberg (uncertainty), Born (probability interpretation).
• Schrödinger equation treats electrons as matter-waves; solutions = orbitals (probability clouds).
• Heisenberg Uncertainty Principle
  \Delta x\,\Delta p \ge \frac{\hbar}{2}
• Electrons described by four quantum numbers (n, l, ml, ms) rather than fixed paths.

Modern View of Atomic Structure

• Nucleus (≈ 10^{-15}\,\text{m} diameter)
  • Protons (+1) & neutrons (0); nearly all atomic mass.
• Electron cloud (≈ 10^{-10}\,\text{m} atom radius)
  • Electrons (−1, mass 9.11\times10^{-31}\,\text{kg}\;\approx 1/1836\,m_p).
  • Occupy orbitals—regions of highest probability, not orbits.

Properties & Roles of Electrons

• Negligible mass but occupy most atomic volume.
• Govern
  • Chemical bonding (ionic, covalent, metallic, coordinate).
  • Electrical/thermal conductivity.
  • Periodic trends & valence.

Quantum Numbers

• Unique “address” of every electron = (n, l, ml, ms).

Principal Quantum Number (n)

• Energy level/shell; n = 1,2,3\,…
• Larger n → higher energy, larger orbital, farther from nucleus.
  • K (1), L (2), M (3), N (4)… shells.

Azimuthal / Angular-Momentum Quantum Number (l)

• Sub-shell shape; l = 0\text{ to }(n-1).
  • l=0 s (spherical)
  • l=1 p (dumbbell)
  • l=2 d (cloverleaf)
  • l=3 f (complex)
• Sub-shell orbital count: s 1, p 3, d 5, f 7.

Magnetic Quantum Number (m_l)

• Orientation; m_l = -l \to 0 \to +l.
  • Example: for l = 1 → ml = -1,0,+1 (px, py, pz).

Spin Quantum Number (m_s)

• Electron spin direction: +\tfrac12 (↑) or -\tfrac12 (↓).
• Max two e⁻ per orbital with opposite spins.

Example : Electron in a 3p orbital

• n = 3 (M-shell)
• l = 1 (p)
• m_l = −1 or 0 or +1
• m_s = +½ or −½

Rules Governing Electron Configuration

Aufbau Principle ("building up")

• Electrons fill lowest available energy orbitals first.
• Empirical energy order
  1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s \dots

(n + l) Rule

• Energy ∝ n + l.
• Lower (n + l) fills first; if tie, lower n fills first.

Hund’s Rule of Maximum Multiplicity

• In degenerate orbitals (e.g.
  p, d, f), electrons fill singly with parallel spins before pairing.
• Minimises e⁻–e⁻ repulsion; maximises exchange energy.
  • Example N (Z=7): 1s^2\,2s^2\,2p^3 → all three 2p orbitals contain one unpaired ↑ electron.

Pauli Exclusion Principle

• No two electrons in same atom share all four quantum numbers.
• Consequence: max 2 electrons/orbital with opposite spins.

Expressing Electron Configurations

Standard (Spectroscopic) Notation

• Series of orbital labels with superscript electron counts.
  • Carbon (Z = 6): 1s^2\,2s^2\,2p^2.

Orbital Diagram (boxes & arrows)

• Box = orbital; ↑ or ↓ = electron spin.
  • C example: 1s [↑↓] 2s [↑↓] 2p [↑][ ][ ].

Noble-Gas (Core) Notation

• Replace filled inner shells by closest noble-gas symbol.
  • Cl (Z = 17): [Ne]\,3s^2\,3p^5.

Electron Configuration & the Periodic Table

Table Structure

• Period = principal quantum number (valence shell).
• Group = identical valence configuration → similar chemistry.
• Blocks
  • s (Groups 1–2), p (13–18), d (3–12, transition), f (lanth./actin.).

Major Periodic Trends & Rationales

• Atomic radius: ↓ across period (↑ nuclear pull), ↑ down group (more shells).
• Ionisation energy: ↑ across, ↓ down (shielding).
• Electron affinity & electronegativity: become more negative/stronger across; weaken down.

Illustrative Cases

• Na (Z = 11): [Ne]3s^1
  • One valence e⁻ → large radius, low IE, highly reactive metal.
• Cl (Z = 17): [Ne]3s^2\,3p^5
  • 7 valence e⁻ → high EN, strong oxidiser.

Chemical Reactivity & Bonding

Valence Electrons

• Outermost-shell electrons; dictate bonding & ion formation.
• O (Z = 8): 1s^2\,2s^2\,2p^4 → 6 valence e⁻ → seeks 2 more → forms two covalent bonds (e.g., H₂O).

Metals vs Non-metals

• Metals (left): few valence e⁻, low IE → lose e⁻ → cations (e.g., Na⁺, Mg²⁺).
• Non-metals (right): high EN/EA → gain e⁻ → anions (F⁻, O²⁻).

Octet Rule & Exceptions

• Atoms strive for noble-gas valence (8 e⁻) for stability.
  • Na → Na⁺ achieves [Ne]; Cl → Cl⁻ achieves [Ar].
• Exceptions: H/He (duet), transition metals, expanded octets (>8, period 3+).

Major Bond Types

• Ionic: electron transfer metal + non-metal → electrostatic lattice (NaCl).
• Covalent: shared electron pairs between non-metals (H₂O, CH₄).
• Coordinate (dative) covalent: both electrons donated by one atom (NH₄⁺).
• Metallic: delocalised e⁻ “sea” in metal lattice → conductivity & malleability.

Coordination Chemistry (Transition Metals)

• Transition metals have variable oxidation states & vacant/partial d-orbitals.
• Form complex ions by accepting lone-pair donation from ligands → coordinate bonds.
  • Ligand: molecule/ion with donor atom & lone pair (H₂O, NH₃, CN⁻).
  • Coordination number = number of donor atoms attached.
  • Example: [Fe(CN)_6]^{3-}
  • Central Fe³⁺, 6 CN⁻ ligands, coordination = 6, octahedral geometry.

Sample Tutorial Questions (Extract)

• 1 Dalton proposed first scientific atomic theory.
• 2 Dalton’s theory did NOT include sub-atomic particles.
• 3 Thomson discovered the electron.
• 4 Thomson’s model = “plum pudding”.
• 5 Gold-foil experiment → nucleus discovery.
• 6 Rutherford: most atomic volume = empty space.
• 7 Limitation: could not explain e⁻ stability (spiral).
• 8 Bohr introduced quantised energy levels.
• 9 Bohr explained hydrogen atom spectra accurately.
• 10 … etc up to 36 (covering quantum numbers, orbital counts, rules, configurations, periodic & subatomic facts).
  • Examples
  • 15 Number of p-orbitals per shell = 3.
  • 17 f sub-shell has 7 orbitals.
  • 18 Max electrons for n = 3 shell = 2n^2 = 18.
  • 21 Aufbau Principle: lowest energy orbitals fill first.
  • 24 Correct configuration of O = 1s^2\,2s^2\,2p^4.
  • 28 4d subshell holds 10 electrons.

Key Equations & Numerical Facts

• Hydrogen energy: E_n = -\frac{13.6\,\text{eV}}{n^2}.
• Uncertainty: \Delta x\,\Delta p \ge \frac{\hbar}{2}.
• Electron mass: 9.11\times10^{-31}\,\text{kg} \approx 1/1836\,m_p.
• Nucleus size ≈ 10^{-15}\,\text{m}; atom ≈ 10^{-10}\,\text{m}.

Ethical & Practical Implications

• Quantum model enables modern spectroscopy, semiconductor design, MRI, quantum computing.
• Recognising probabilistic nature prevents misconceptions (no classical orbits → avoids planetary analogy misuse).
• Safety in nuclear/chemical industries relies on accurate sub-atomic knowledge.

Connections & Significance

• Historical progression mirrors scientific method: hypothesis → experiment → refinement.
• Quantum numbers bridge abstract mathematics (solutions to Schrödinger’s equation) with tangible periodic trends.
• Electron configuration provides predictive power for chemistry, materials science, biochemistry, and nanotechnology.

Next Topic Preview

• Having established quantum numbers & filling rules, subsequent study will focus on detailed electron configurations, exceptions (Cr, Cu anomalies), and their consequences for chemical bonding & spectroscopy.