9-17 Chem 200 Notes: Atomic Structure and Periodic Trends

Electronic Structure of Atoms

  • Sublevel capacities: s:2, p:6, d:10, f:14.s:2,\, p:6,\, d:10,\, f:14.
  • Aufbau principle: electrons fill the lowest energy subshells first and build up from there.
    • Common filling sequence (partial): 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6…1s^2\ 2s^2\ 2p^6\ 3s^2\ 3p^6\ 4s^2\ 3d^{10}\ 4p^6\ldots
  • The Bohr model and development of quantum theory underpin modern electron configurations.

Writing Electron Configurations

  • Ground-state configurations can be written fully or condensed using noble-gas cores.
  • Example: Silicon (Si) ground state in full notation is 1s22s22p63s23p21s^22s^22p^63s^23p^2 and in condensed form [Ne] 3s23p2.[\text{Ne}]\,3s^23p^2.
  • For elements, use the Aufbau principle and Hund’s rules to determine the correct arrangement.

Valence vs Core Electrons

  • Valence electrons: electrons in the highest principal quantum number (largest $n$); most chemically important.
  • Core electrons: electrons in filled, lower-energy levels.

Electron Configurations for Groups

  • Group 2 (alkaline earth) elements have 2 valence electrons: e.g., Be:[He] 2s2,Mg:[Ne] 3s2,Ca:[Ar] 4s2.\text{Be}: [\text{He}]\,2s^2,\quad \text{Mg}: [\text{Ne}]\,3s^2,\quad \text{Ca}: [\text{Ar}]\,4s^2.
  • Group 7 (halogens) have 7 valence electrons: e.g., F:[He] 2s22p5,Cl:[Ne] 3s23p5.\text{F}: [\text{He}]\,2s^22p^5,\quad \text{Cl}: [\text{Ne}]\,3s^23p^5.

Orbital Filling Rules

  • Hund’s Rule: with degenerate orbitals, maximize the number of unpaired electrons with parallel spins.
  • Pauli Exclusion Principle: no two electrons can have the same set of quantum numbers.
  • Pairing occurs only after all subshell orbitals in a given sublevel have one electron each.

Atomic Properties: Trends (Overview)

  • Atomic radii, ionic radii, ionization energy, and electron affinity show periodic trends driven by effective nuclear charge ($Z_{ ext{eff}}$) and shielding.
  • Key factors:
    • Zeff increases across a period → radius tends to decrease across a period.
    • Radius increases down a group due to increasing principal quantum number $n$.
  • For main-group elements, radii increase down a group and generally decrease across a period; transition metals are less systematic.

Atomic Radii and Ionic Radii

  • Atomic radius: half the distance from nucleus to boundary of surrounding electron cloud; environment affects measured value.
  • Ionic radius: radius of ions; environment-dependent; cations are smaller than their neutral atoms; anions larger.
  • Main trends:
    • Cations: smaller than parent atoms (e.g., Li$^+$ < Li).
    • Anions: larger than parent atoms (e.g., F$^-$ > F).
    • Ionic radii increase down a group; for isoelectronic series, radius decreases with increasing nuclear charge.

Isoelectronic Ions (same electron count)

  • In a set of isoelectronic ions, the one with the greatest nuclear charge ($Z$) has the smallest radius.
  • Example concept: for ions with the same number of electrons, radius order correlates with effective nuclear charge.

Ionization Energy (IE)

  • Definition: energy required to remove an electron from a gas-phase atom or ion.
  • Notation: A(g)→A+(g)+e−(g)ΔE=IE1.A(g) \rightarrow A^+(g) + e^-(g)\quad \Delta E = IE_1.
  • Successive IE: IE1 < IE2 < IE_3 < \cdots.
  • Trends (general): IE tends to increase across a period and decrease down a group; large jumps occur when a core electron is removed.
  • Example concept: removing a core electron requires substantially more energy than removing a valence electron.

Electron Affinity (EA)

  • Definition: energy change when an electron is added to a gas-phase atom or ion.
  • Notation: A(g)+e−(g)→A−(g)ΔE=EA1.A(g) + e^-(g) \rightarrow A^-(g)\quad \Delta E = EA_1.
  • EA values can be positive or negative; trends are less straightforward than IE or radii.

Ionic and Covalent Bonding; Polyatomic Ions

  • Ionic bonds: metal + non-metal; electrons transferred from metal to non-metal.
  • Covalent bonds: non-metals share electrons.
  • Polyatomic ions: ions composed of more than one atom (e.g., (\text{CO}3^{2-}), (\text{SO}4^{2-})).
  • Naming conventions:
    • Ionic compounds: name metal followed by nonmetal with -ide if simple (e.g., NaCl = sodium chloride).
    • Covalent compounds: use prefix system to denote number of atoms (e.g., (\text{PCl}_3) = phosphorous trichloride).

Periodic Table: Organization and Historical Context

  • Periodic law (modern): properties vary periodically with atomic number; Moseley established the role of atomic number as the basis for periodicity.
  • The table is organized into: groups (columns) and periods (rows); main-group, transition metals, lanthanides, and actinides.
  • Noble gases are Group 18; alkali metals are Group 1; alkaline earths are Group 2; halogens are Group 17.
  • The table reflects recurring chemical properties across groups and periods.

Quick Concept Checks

  • Which element forms a stable 3+ cation most readily? Group 3 elements (e.g., Sc, Al) tend to form +3 cations; Sc and Al both commonly form +3.
  • For isoelectronic ions, which has the largest radius: the one with the smallest nuclear charge.
  • When writing electron configurations for ions, remember to remove electrons from the highest energy level first (aufbau with ionization).

Useful Notation recap

  • Electron configuration principle notation: 1s22s22p6…1s^22s^22p^6\ldots
  • Condensed/notational shorthand: [Core]valence sublevels[\text{Core}]\text{valence sublevels}
  • Ionization: A(g)→A+(g)+e−(g)IE<em>1A(g) \rightarrow A^+(g) + e^-(g)\quad IE<em>1; A(g)+e−(g)→A−(g)EA</em>1A(g) + e^-(g) \rightarrow A^-(g)\quad EA</em>1
  • Sublevel capacities: s→2, p→6, d→10, f→14s\to 2,\, p\to 6,\, d\to 10,\, f\to 14