2.2 Atomic theory and models

Atomic theory and models form the foundation of our understanding of matter. From Dalton's indivisible atoms to the quantum mechanical model, scientists have refined our view of atomic structure over time. These models explain how atoms behave and interact, shaping our grasp of chemistry.

The evolution of atomic models reflects the progress of scientific inquiry. Each new discovery, from electrons to the nucleus, has deepened our knowledge of atomic structure. This journey through atomic theory connects directly to our understanding of elements and their properties.

Atomic Theory: Development and Evolution

Dalton's Atomic Theory

• Proposed that all matter is composed of indivisible particles called atoms
• Atoms of the same element are identical, while atoms of different elements have different properties
• Compounds are formed by a combination of atoms
• Laid the foundation for modern atomic theory, but did not account for subatomic particles or the internal structure of atoms

Discovery of the Electron and the Plum Pudding Model

• J.J. Thomson discovered the electron through his cathode ray tube experiments
• Led to the plum pudding model of the atom, which proposed that electrons were embedded in a positively charged "pudding"
• This model represented the atom as a positively charged sphere with negatively charged electrons scattered throughout
• While an improvement over Dalton's model, the plum pudding model did not accurately describe the internal structure of the atom

Rutherford's Nuclear Model

• Rutherford's gold foil experiment demonstrated the existence of a small, dense, positively charged nucleus at the center of the atom
• In this experiment, alpha particles were fired at a thin gold foil, and most passed through, but some were deflected at large angles, indicating a concentrated positive charge
• This led to the nuclear model of the atom, with electrons orbiting a positively charged nucleus
• The nuclear model provided a more accurate representation of the atom's internal structure but did not explain the stability of atoms or the discrete energy levels of electrons

Bohr's Model and the Introduction of Quantum Theory

• Bohr's model of the atom proposed that electrons orbit the nucleus in fixed, quantized energy levels
• Electrons can move between these levels by absorbing or emitting specific amounts of energy, resulting in the emission of light at specific wavelengths
• This model successfully explained the spectral lines of hydrogen and introduced the concept of quantized energy states
• However, Bohr's model failed to accurately describe the behavior of atoms with more than one electron and did not fully incorporate the principles of quantum mechanics

The Quantum Mechanical Model

• The development of quantum mechanics led to the modern understanding of the atom
• In this model, the behavior of electrons is described using wave functions and probability distributions
• The quantum mechanical model accounts for the wave-particle duality of electrons and the uncertainty principle, providing a more accurate and complete description of atomic structure
• This model forms the basis for our current understanding of atomic and molecular structure, chemical bonding, and the properties of matter

Bohr Model vs Quantum Mechanical Model

Electron Behavior and Energy Levels

• Bohr model: Electrons orbit the nucleus in fixed, circular orbits with quantized energy levels
• Quantum mechanical model: Electrons are described as probability distributions in three-dimensional space, with their behavior governed by wave functions
• Bohr model: Electrons can only transition between energy levels by absorbing or emitting specific amounts of energy
• Quantum mechanical model: Electrons can exist in a superposition of multiple energy states, with their energy determined by the Schrödinger equation

Accuracy and Applicability

• Bohr model: Successfully explained the spectral lines of hydrogen but failed to accurately describe the behavior of atoms with more than one electron (e.g., helium, lithium)
• Quantum mechanical model: Accurately describes the behavior of all atoms, regardless of the number of electrons
• Bohr model: A semi-classical model that incorporates some aspects of quantum theory, such as quantized energy levels
• Quantum mechanical model: A fully quantum description of the atom, accounting for wave-particle duality and the uncertainty principle

Atomic Orbitals and Electron Configuration

Atomic Orbitals

• Atomic orbitals are mathematical functions that describe the probability distribution of an electron in an atom
• They represent the regions in space where an electron is most likely to be found
• Orbitals are characterized by four quantum numbers:
  1. Principal quantum number (n): Determines the energy and size of the orbital (e.g., 1, 2, 3)
  2. Angular momentum quantum number (l): Determines the shape of the orbital (e.g., s, p, d, f)
  3. Magnetic quantum number (ml): Determines the orientation of the orbital in space (e.g., px, py, pz)
  4. Spin quantum number (ms): Describes the spin of the electron (e.g., +1/2, -1/2)
• The shapes of orbitals are determined by the angular momentum quantum number:
  • s orbitals: Spherical
  • p orbitals: Dumbbell-shaped (px, py, pz)
  • d and f orbitals: More complex shapes (e.g., dxy, dxz, dyz, dx2-y2, dz2)

Electron Configuration and Energy Ordering

• The electron configuration of an atom describes the distribution of electrons among the available orbitals
• The energy of an orbital increases with increasing principal quantum number (n)
• Within a given principal quantum number, the energy of the orbitals increases in the order: s < p < d < f
• Example: The electron configuration of carbon (6 electrons) is 1s² 2s² 2p², meaning two electrons in the 1s orbital, two in the 2s orbital, and two in the 2p orbitals
• The relationship between atomic orbitals and electron configuration is crucial for understanding the chemical properties and reactivity of elements

Electron Configuration: Aufbau, Hund's Rule, and Pauli Exclusion

Aufbau Principle

• The Aufbau principle states that electrons fill orbitals in order of increasing energy, starting with the lowest energy orbital (1s) and progressing to higher energy orbitals
• The order of filling is determined by the n + l rule, with lower values of n + l being filled first
• Example: The filling order for the first few orbitals is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f
• The Aufbau principle provides a systematic way to determine the ground state electron configuration of an atom

Hund's Rule

• Hund's rule states that when there are multiple orbitals of equal energy (degenerate orbitals), electrons will occupy these orbitals singly with parallel spins before pairing up with opposite spins
• This minimizes electron-electron repulsion and results in a lower energy configuration
• Example: In the electron configuration of nitrogen (7 electrons), the three 2p electrons will occupy separate 2p orbitals with parallel spins before pairing up: 1s² 2s² 2p³
• Hund's rule helps predict the most stable electron configuration and the magnetic properties of atoms

Pauli Exclusion Principle

• The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers
• This means that each orbital can hold a maximum of two electrons with opposite spins
• Example: In the electron configuration of helium (2 electrons), both electrons occupy the 1s orbital but have opposite spins: 1s²
• The Pauli exclusion principle is a fundamental concept in quantum mechanics and is essential for understanding the structure and properties of atoms and molecules

Writing Electron Configurations for Atoms and Ions

• To write an electron configuration, list the orbitals in order of increasing energy and fill them with electrons according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle
• Example: The electron configuration of chlorine (17 electrons) is 1s² 2s² 2p⁶ 3s² 3p⁵
• For ions, first write the electron configuration of the neutral atom, then add or remove electrons as necessary:
  • For cations (positive ions), remove electrons starting with the highest energy electrons
  • For anions (negative ions), add electrons to the next available orbital
• Example: The electron configuration of the chloride ion (Cl⁻, 18 electrons) is 1s² 2s² 2p⁶ 3s² 3p⁶