🌀Principles of Physics III Unit 8 – Atomic Structure

Key Concepts and Terminology

• Atom smallest unit of matter that retains the properties of an element
• Proton positively charged subatomic particle located in the nucleus
• Neutron neutral subatomic particle located in the nucleus
• Electron negatively charged subatomic particle orbiting the nucleus
  • Responsible for chemical bonding and electrical conductivity
• Atomic number (Z) number of protons in an atom's nucleus
• Mass number (A) total number of protons and neutrons in an atom's nucleus
• Isotopes atoms of the same element with different numbers of neutrons
• Quantum mechanics mathematical framework describing the behavior of matter and energy at the atomic and subatomic scales

Historical Development of Atomic Theory

• Dalton's atomic theory (early 19th century) proposed that all matter is composed of indivisible particles called atoms
• Cathode ray experiment (J.J. Thomson, 1897) discovered the electron and proposed the "plum pudding" model of the atom
• Millikan's oil drop experiment (1909) determined the charge and mass of the electron
• Rutherford's gold foil experiment (1909) discovered the atomic nucleus and proposed the nuclear model of the atom
  • Alpha particles were deflected by a small, dense, positively charged nucleus
• Bohr's atomic model (1913) introduced the concept of quantized energy levels and electron orbits
  • Explained the discrete emission spectrum of hydrogen
• Wave-particle duality (de Broglie, 1924) proposed that particles can exhibit wave-like properties
• Heisenberg's uncertainty principle (1927) stated that the position and momentum of a particle cannot be simultaneously determined with perfect accuracy

Fundamental Particles and Their Properties

• Proton
  • Charge +1 elementary charge (e)
  • Mass 1.67 × 10^-27 kg (approximately 1,836 times the mass of an electron)
• Neutron
  • Charge 0
  • Mass 1.67 × 10^-27 kg (slightly more massive than a proton)
• Electron
  • Charge -1 elementary charge (e)
  • Mass 9.11 × 10^-31 kg
• Quarks fundamental constituents of protons and neutrons
  • Up quark (charge +2/3 e) and down quark (charge -1/3 e)
  • Proton composed of two up quarks and one down quark (uud)
  • Neutron composed of one up quark and two down quarks (udd)
• Leptons elementary particles not composed of quarks (electron is a type of lepton)

Atomic Models and Their Evolution

• Dalton's solid sphere model atoms are indivisible and indestructible solid spheres
• Thomson's plum pudding model atoms are a positively charged "pudding" with negatively charged electrons embedded throughout
• Rutherford's nuclear model atoms consist of a small, dense, positively charged nucleus surrounded by electrons
  • Explained the results of the gold foil experiment
• Bohr's atomic model electrons orbit the nucleus in discrete, quantized energy levels
  • Electrons can transition between energy levels by absorbing or emitting specific amounts of energy
• Quantum mechanical model (Schrödinger, Heisenberg) atoms described by wave functions and probability distributions
  • Electron behavior governed by the Schrödinger equation

Quantum Mechanical Description of Atoms

• Wave function (Ψ) mathematical description of the quantum state of a system
  • Provides information about the probability of finding an electron at a given location
• Schrödinger equation describes the behavior of a quantum system and its wave function
  • $\hat{H}\Psi = E\Psi$, where $\hat{H}$ is the Hamiltonian operator and $E$ is the energy of the system
• Orbital region of space where an electron is likely to be found
  • Characterized by quantum numbers (n, l, m_l, m_s)
• Quantum numbers
  • Principal quantum number (n) determines the energy and size of the orbital
  • Angular momentum quantum number (l) determines the shape of the orbital (s, p, d, f)
  • Magnetic quantum number (m_l) determines the orientation of the orbital in space
  • Spin quantum number (m_s) describes the intrinsic angular momentum of the electron (±1/2)
• Pauli exclusion principle no two electrons in an atom can have the same set of quantum numbers

Electron Configuration and Orbitals

• Electron configuration arrangement of electrons in an atom's orbitals
  • Notation 1s^2 2s^2 2p^6 3s^2 3p^6 (for argon)
• Aufbau principle electrons fill orbitals in order of increasing energy
• Hund's rule electrons occupy degenerate orbitals singly before pairing, with parallel spins
• Orbital shapes
  • s orbital spherical
  • p orbitals dumbbell-shaped (px, py, pz)
  • d orbitals cloverleaf and double-dumbbell shapes (dxy, dyz, dxz, dx^2-y^2, dz^2)
  • f orbitals complex shapes

Periodic Table and Atomic Trends

• Periodic table arrangement of elements based on their atomic number and electron configuration
  • Rows (periods) correspond to the principal quantum number (n)
  • Columns (groups) contain elements with similar electron configurations and chemical properties
• Atomic radius tends to decrease from left to right across a period and increase down a group
  • Effective nuclear charge increases across a period, pulling electrons closer to the nucleus
• Ionization energy energy required to remove an electron from an atom
  • Tends to increase from left to right across a period and decrease down a group
• Electronegativity ability of an atom to attract electrons in a chemical bond
  • Tends to increase from left to right across a period and decrease down a group
• Metallic character tends to decrease from left to right across a period and increase down a group

Applications and Real-World Relevance

• Spectroscopy techniques based on the interaction of atoms with electromagnetic radiation
  • Used to identify elements and compounds, study atomic and molecular structure, and analyze materials
• Lasers rely on the stimulated emission of photons from excited atomic states
  • Applications in medicine (surgery, dentistry), manufacturing (cutting, welding), and technology (optical storage, fiber-optic communication)
• Atomic clocks most precise timekeeping devices, based on the frequency of atomic transitions
  • Used in GPS navigation, telecommunications, and scientific research
• Quantum computing utilizes the quantum states of atoms or other quantum systems to perform calculations
  • Potential to solve complex problems much faster than classical computers
• Nuclear energy fission of heavy atomic nuclei (uranium, plutonium) releases large amounts of energy
  • Used in nuclear power plants to generate electricity
• Radiation therapy uses high-energy radiation (X-rays, gamma rays) to target and destroy cancer cells
  • Relies on the ionizing effects of radiation on atomic and molecular structure