Atomic Structure & Electron Configuration – Week 2 Lecture

Administrative & Contextual Comments

  • Lecturer: Dr. Scott Stewart (Chem 01/2002, Week 2)
  • Previous lecture (Prof. Flemati) covered: atomic wave-equation for H, quantum numbers n,l,m_l.
  • Today’s focus:
    • Historical evolution of atomic structure models.
    • Quantum numbers (adding spin m_s) & orbital shapes.
    • Energy ordering, filling rules & electron configuration.
    • Links to chemical reactivity (organic molecules, e.g.
      trinitrotoluene – TNT).

Recap of Hydrogen‐Atom Wave Equation & Quantum Numbers

  • Schrödinger equation → wave-function \psi → probability distribution (orbitals).
  • Quantum numbers (3 original + 1 added today):
    • n (principal): overall shell/energy level; integers 1,2,3…
    • l (angular momentum): orbital shape; 0\le l \le n-1
    • l=0 → s, l=1 → p, l=2 → d …
    • ml (magnetic): orientation in 3-D space; -l \le ml \le +l (x, y, z directions etc.).
    • m_s (spin): +½ or –½; introduced in 1920s → two electrons per orbital with opposite spin (spin pairing).

From Planetary (Bohr) Model to Quantum Model

  • High-school “planetary” picture: electrons orbit nucleus in circular shells.
  • Shortcomings (why abandoned):
    • Cannot predict electron-electron repulsion.
    • Fails for nuclear–electron attractions beyond simple H.
    • Implies electrons only on fixed rings; quantum mechanics allows probability in between.
  • Modern view: electron density clouds shaped by \psi^2.

Shells, Subshells & Maximum Electron Count

  • Shell numbers correspond to n values.
  • Each shell can hold 2n^2 electrons.
    • n=1 → 2; n=2 → 8; n=3 → 18; n=4 → 32.
  • Subshells = sets of orbitals with same n & l.
  • Each individual orbital holds 2 e⁻ (Pauli Exclusion).

Shapes & Orientations of Orbitals

  • s (spherical): 1 orientation ( m_l=0 ). Radii grow with n (1s < 2s < 3s …).
  • p (dumb-bell): 3 orientations (px, py, p_z). Node at nucleus; probability lobes on either side.
  • d: 5 orientations.
    • 4 clover-leaf shapes in x-y-z planes; 1 “donut + dumbbell” (d_{z^2}).
  • All shapes arise mathematically from solutions to Schrödinger equation.
  • Electron‐location phrase: “95 % probability volume”.

Degeneracy Concept

  • Orbitals with identical energy = “degenerate”.
  • In hydrogen (single electron) all subshells with same n are degenerate: 2s = 2p = 3s = 3d …
  • Multi-electron atoms: inter-electron repulsion breaks degeneracy (energy ordering 1s < 2s < 2p < 3s …).

Energy Ordering & Orbital Filling Rules

Diagrams

  • Energy ladder diagram: vertical axis = energy; squares = individual orbitals.
  • Hydrogen example: only 1e⁻ → placed in lowest energy (1s) for ground state; higher empty orbitals still exist for excitation & bonding.

Three Filling Rules

  1. Aufbau Principle (“build-up”): fill lowest energy orbitals first.
  2. Pauli Exclusion Principle: max 2 e⁻ per orbital, must have opposite spin.
  3. Hund’s Rule: within degenerate set (e.g. three 2p), place one e⁻ in each with parallel spins before pairing; pairing costs extra energy.

Visual mnemonic (textbook diagram)

  • Diagonal arrows 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p …

Orbital Notation & Symbolism

  • General label: n\,l^{\text{electron count}} (e.g. 4p^5).
  • For p or d, can specify orientation: 4px, 4py, 4p_z.
  • Example decomposition: 4p^5 = 4px^2\,4py^2\,4p_z^1 (total 5 e⁻ across 3 degenerate orbitals).
  • Electron symbol: half arrow ↑ or ↓.

Worked Examples

1 e⁻ Hydrogen Configuration

  • 1s^1 (↑)
  • Higher orbitals empty but present → excitation & bonding possibility.

Lithium (Z = 3)

  • Fill: 1s^2\,2s^1.
  • 1s electrons spin-paired; 2s lone electron is valence → dictates Li reactivity.

Silicon (Z = 14) – Classroom Exercise

  • Stepwise filling respecting rules:
    • 1s^2 (↑↓)
    • 2s^2 (↑↓)
    • 2p^6 (↑ ↑ ↑ ↓ ↓ ↓)
    • 3s^2 (↑↓)
    • 3p^2 (↑ ↑ _)
  • Shorthand (core [Ne]): [Ne]\,3s^2\,3p^2.

Periodic Table Connections

  • Electron configuration printed (italic) under each element symbol; shorthand uses preceding noble gas in brackets.
  • Blocks:
    • s-block (Groups 1–2 + He): valence in s.
    • p-block (Groups 13–18): valence in p.
    • d-block (transition metals): valence filling d.
  • Similar valence configurations → similar chemistry:
    • Alkali metals (Li, Na, K, Rb, Cs, Fr): one s-electron; violent water reactivity (video of Cs + H₂O recommended).
    • Chalcogens (O, S, Se …): six valence electrons → analogous functional groups in organic chemistry.

Valence vs Core Electrons

  • Valence = electrons in outermost n; control bonding & reactivity.
  • Core = inner shells (lower n), closer to nucleus.
  • Example O: 1s^2 core (2 e⁻); 2s^2\,2p^4 valence (6 e⁻).

Effective Nuclear Charge (Shielding) – Z^*

  • Valence e⁻ feel reduced attraction due to inner e⁻ shielding.
  • Define: Z^* = Z - S where
    • Z = actual proton count (nuclear charge).
    • S = shielding constant via Slater’s rules.
  • Slater parameters (approx.):
    • 0.35 per other valence e⁻ in same shell.
    • 0.85 per e⁻ in shell n-1.
    • 1.00 per e⁻ in deeper shells.
  • Silicon example:
    • Z=14.
    • S = 3(0.35) + 8(0.85) + 2(1.00) = 9.8.
    • Z^* = 14 - 9.8 \approx 4.2.
  • Trends:
    • Z^* increases left → right across a period (poor extra shielding; stronger nuclear pull).
    • Higher Z^* ⇒ smaller atomic radius; higher ionization energy.

Ionization Energy

  • Definition: energy required to remove (or promote) an electron from a gaseous atom or ion (usually first valence e⁻).
  • Mirrors Z^* trend: increases across period, decreases down group.

Reactivity Examples & Organic Connection

  • TNT (Trinitrotoluene): toluene core + 3 nitro groups. Highly reactive/explosive → seeks rapid formation of N2 & O2 gases.
  • Bond-formation illustration: lone H orbital can overlap empty higher orbital of C to form C–H bond (molecular orbital concept).
  • Understanding orbital energies allows prediction of organic reaction pathways.

Summary of Key Take-Aways

  • Quantum numbers fully describe electron state; spin (m_s) completes set.
  • Shapes (s, p, d) and orientations stem from Schrödinger wave-functions.
  • Filling order governed by Aufbau, Pauli, Hund.
  • Electron configurations rationalize periodic trends, reactivity & bonding (vital for forthcoming organic chemistry content).
  • Shielding & effective nuclear charge provide quantitative handle on atomic size & ionization energy.