CH 7 (11/20) (PG 1-6)

Chemistry and Chemical Reactivity: Chapter 7 - The Structure of Atoms and Periodic Trends

Arrangement of Electrons in Atoms

• Electrons in atoms are arranged in a hierarchical structure comprising:

  • Shells (n): Principal energy levels where electrons reside.

  • Subshells (l): Types of orbitals within shells, defined by angular momentum.

  • Orbitals (ml): Specific regions within subshells where electrons are likely to be found.

Pauli Exclusion Principle

• Definition: An orbital in an atom is characterized by a set of three quantum numbers: (n, l, m_l).

• Statement: No more than two electrons can be assigned to the same orbital. If two electrons occupy the same orbital, they must have opposite spins.

• Implication: No two electrons in an atom can possess the same set of four quantum numbers (n, l, ml, ms), where (m_s) is the spin quantum number.

Quantum Numbers & Electron Orbitals

• Quantum Numbers Definition: Terms derived from the Schrödinger equation that describe the state of an electron, effectively serving as its "address".

• Each electron in an orbital is defined by its own set of three quantum numbers:

  • Principal Quantum Number (n): Values of n = 1, 2, 3, 4, … to infinity; indicates the shell.

  • Orbital Angular Momentum Quantum Number (l): Values from 0 to n - 1; indicates the subshell.

  • Magnetic Quantum Number (m_l): Integer values from -l to +l; specifies the individual orbital.

Single-Electron Atom Energy Levels

• In a hydrogen atom (1-electron), the orbitals of a subshell are equal in energy and are thus termed degenerate.

Atomic Subshell Energies & Electron Assignments in Multi-electron Atoms

• General Rules for Electron Assignments:

  • Electrons are assigned to subshells in increasing order of the sum of principal and angular momentum quantum numbers (n + l).

  • For subshells with the same n + l value, electrons fill the subshell with the lower n first.

Multi-Electron Atom Energy Levels

• The energy hierarchy for orbitals is such that:

  • Comparison: The 4s-orbital has a higher energy than the 3p-orbital but lower than the 3d-orbital.

  • Calculating n + l values:

    • For 4s: n + l = 4 + 0 = 4

    • For 3d: n + l = 3 + 2 = 5

Order of Subshell Energies in a Multi-Electron Atom

• The filling order reflects interactions due to screening and electron-electron repulsions, indicating that the 4s orbital is filled prior to 3d.

Effective Nuclear Charge (Z*)

• Definition: The charge experienced by the outermost electrons of an atom, factoring in shielding from inner electrons.

• Concept of Shielding: Electrons closer to the nucleus reduce the effective nuclear charge experienced by outer electrons.

• Examples of effective nuclear charge calculations:

  • For Lithium (Li): Z^* = 3 - 2 = 1 (3 protons, 2 inner electrons)

  • For Beryllium (Be): Z^* = 4 - 2 = 2

  • For Boron (B): Z^* = 5 - 2 = 3

• Trend in Effective Nuclear Charge:

  • Z* increases across a period due to increased nuclear charge while the number of inner electrons remains relatively stable.

Variations in Z* for Different Subshells

• The values of Z* also vary depending on subshell type:

  • Systematic difference: ns > np > nd > nf (where n is the principal quantum number).

  • Higher Z* correlates with lower energy for subshells: ns < np < nd < nf.

Electron Configurations

• Definition: Configuration describes how electrons are arranged around atomic nuclei.

• Aufbau Principle: Electrons fill subshells in order of increasing energy.

• Hund's Rule: Degenerate orbitals fill singly first with parallel spins before pairing occurs.

• Pauli Exclusion Principle Reminder: Each orbital can hold a maximum of two electrons, which must have opposite spins.

Shell and Orbital Capacities

• Subshell Capacities:

  • s orbitals can hold 2 electrons.

  • p orbitals can hold up to 6 electrons.

  • d orbitals can hold up to 10 electrons.

  • f orbitals can hold up to 14 electrons.

Numbering System for Electron Configurations

• Representative notation:

  • Numbers (1, 2, 3…) represent the principal quantum numbers (shell number).

  • Lower-case letters (s, p, d, f) denote the angular momentum quantum number (orbital type).

  • Superscripts indicate the number of electrons in that subshell.

Examples of Electron Configurations

• Helium:

  • SPDF Notation: 1s²

  • Box Notation: 1s

• Lithium (Li): 3 electrons

  • SPDF Notation: 1s² 2s¹

• Beryllium (Be): 4 electrons

  • SPDF Notation: 1s² 2s²

• Boron (B): 5 electrons

  • SPDF Notation: 1s² 2s² 2p¹

• Carbon (C): 6 electrons

  • SPDF Notation: 1s² 2s² 2p²

• Nitrogen (N): 7 electrons

  • SPDF Notation: 1s² 2s² 2p³

• Oxygen (O): 8 electrons

  • SPDF Notation: 1s² 2s² 2p⁴

• Fluorine (F): 9 electrons

  • SPDF Notation: 1s² 2s² 2p⁵

• Neon (Ne): 10 electrons, full 2nd shell

  • SPDF Notation: 1s² 2s² 2p⁶

Orbital Filling: Pauli Principle

• Electrons fill orbitals following the Pauli Exclusion Principle:

  • Upward arrows indicate spin up (↑), and downward arrows indicate spin down (↓).

Electron Configuration in the Third Period

• Aluminum (Al), Atomic number 13:

  • Box Notation: Illustrates orbital filling.

  • SPDF Notation: 1s² 2s² 2p⁶ 3s² 3p¹

Noble Gas Notation

• Definition: Electron configurations of elements can employ the configuration of the nearest preceding noble gas for simplicity:

  • Example for Silicon (Si):

  • Full: 1s² 2s² 2p⁶ 3s² 3p²

  • Noble gas: [Ne] 3s² 3p²

Transition Metals and Electron Configuration

• Transition metals in 4th and 5th periods follow the general electron configuration:

  • (noble ext{ }gas) ns^{x}(n-1)d^{y},

  • where n is the period number and x, y specify particular elements.

  • E.g., Argon (Ar) is the noble gas for n=4, Krypton (Kr) for n=5.

Summary of Valence Electrons

• Main-Group Elements: Valence electrons are defined as the electrons in the outermost shell.

• Transition Metals: Include both the outer shell electrons and d-electrons from the second outermost shell.

• Chemical Reactivity: Valence electrons are involved in chemical reactions, while core electrons remain inert due to their strong attraction to the nucleus.