🫴Physical Science Unit 4 – Atomic Structure

Key Concepts

• Atoms are the fundamental building blocks of matter consisting of protons, neutrons, and electrons
• Atomic number represents the number of protons in an atom's nucleus determines the element's identity
• Mass number is the sum of protons and neutrons in an atom's nucleus
• Isotopes are atoms of the same element with different numbers of neutrons
• Electron configuration describes the arrangement of electrons in an atom's orbitals follows the Aufbau principle, Hund's rule, and the Pauli exclusion principle
• Quantum mechanics explains the behavior of subatomic particles using wave-particle duality and the Heisenberg uncertainty principle
• The periodic table organizes elements based on their atomic number and electron configuration reflects periodic trends in properties

Historical Development

• Ancient Greek philosophers (Democritus, Leucippus) proposed the concept of the atom as the smallest indivisible unit of matter
• John Dalton's atomic theory (1808) stated that elements are composed of indivisible atoms, atoms of the same element are identical, and compounds form by combining atoms in simple whole-number ratios
• J.J. Thomson's cathode ray experiment (1897) led to the discovery of the electron and the "plum pudding" model of the atom
• Ernest Rutherford's gold foil experiment (1909) revealed the existence of the atomic nucleus led to the nuclear model of the atom
• Niels Bohr's model (1913) introduced the concept of electron shells and energy levels explained the hydrogen spectrum
  • Electrons orbit the nucleus in fixed energy levels
  • Electrons can jump between energy levels by absorbing or emitting specific amounts of energy
• James Chadwick discovered the neutron in 1932 completing the modern understanding of atomic structure

Atomic Models

• Dalton's atomic model: Atoms are solid, indivisible spheres
• Thomson's "plum pudding" model: Atoms are spheres of positive charge with embedded negative electrons
• Rutherford's nuclear model: Atoms have a small, dense, positively charged nucleus surrounded by electrons
• Bohr's model: Electrons orbit the nucleus in fixed energy levels can jump between levels by absorbing or emitting energy
  • Explained the hydrogen spectrum
  • Could not accurately describe atoms with more than one electron
• Quantum mechanical model: Electrons occupy orbitals with specific shapes and energies described by wave functions
  • Incorporates the Heisenberg uncertainty principle and wave-particle duality
  • Accurately describes the behavior of electrons in multi-electron atoms

Subatomic Particles

• Protons: Positively charged particles located in the nucleus
  • Charge: +1
  • Mass: 1.67 × 10⁻²⁷ kg (1,836 times the mass of an electron)
• Neutrons: Neutral particles located in the nucleus
  • Charge: 0
  • Mass: 1.67 × 10⁻²⁷ kg (similar to proton mass)
• Electrons: Negatively charged particles orbiting the nucleus
  • Charge: -1
  • Mass: 9.11 × 10⁻³¹ kg (1/1,836 the mass of a proton)
• Quarks: Elementary particles that make up protons and neutrons
  • Up quarks and down quarks combine to form protons (uud) and neutrons (udd)
• Leptons: Elementary particles that include electrons and neutrinos

Electron Configuration

• Electrons occupy orbitals in an atom's electron shells (energy levels)
• Orbitals are described by four quantum numbers: principal (n), angular momentum (l), magnetic (m), and spin (s)
• Aufbau principle: Electrons fill orbitals in order of increasing energy (1s, 2s, 2p, 3s, 3p, 4s, 3d, ...)
• Hund's rule: Electrons occupy degenerate orbitals singly before pairing up with parallel spins
• Pauli exclusion principle: No two electrons in an atom can have the same set of four quantum numbers
• Electron configurations can be written using orbital notation (e.g., 1s²2s²2p⁶) or noble gas notation (e.g., [Ne] 3s²3p³)
• Valence electrons in the outermost shell determine an element's chemical properties and bonding behavior

Isotopes and Atomic Mass

• Isotopes are atoms of the same element with different numbers of neutrons
  • Same atomic number (number of protons) but different mass numbers (protons + neutrons)
• Atomic mass is the weighted average of an element's naturally occurring isotopes
  • Measured in atomic mass units (amu) where 1 amu = 1/12 the mass of a carbon-12 atom
• Relative abundance of isotopes affects an element's atomic mass
  • Example: Chlorine has two main isotopes, Cl-35 (75.77%) and Cl-37 (24.23%), resulting in an atomic mass of 35.45 amu
• Mass spectrometry separates isotopes based on their mass-to-charge ratio used to determine relative abundances

Quantum Mechanics Basics

• Wave-particle duality: Matter exhibits both wave-like and particle-like properties
  • Electrons can behave as waves (interference patterns) or particles (photoelectric effect)
• Heisenberg uncertainty principle: The more precisely the position of a particle is determined, the less precisely its momentum can be known, and vice versa
  • Represented by the equation: $\Delta x \Delta p \geq \frac{h}{4\pi}$, where $h$ is Planck's constant
• Schrödinger equation: Describes the wave function of a quantum-mechanical system determines the probability of finding a particle at a given location
  • $\hat{H}\Psi = E\Psi$, where $\hat{H}$ is the Hamiltonian operator, $\Psi$ is the wave function, and $E$ is the energy of the system
• Quantum numbers: Describe the state of an electron in an atom
  • Principal quantum number (n): Determines the energy and size of the orbital
  • Angular momentum quantum number (l): Determines the shape of the orbital
  • Magnetic quantum number (m): Determines the orientation of the orbital in space
  • Spin quantum number (s): Describes the intrinsic angular momentum (spin) of the electron

Applications and Real-World Relevance

• Spectroscopy: Analysis of emission and absorption spectra to identify elements and compounds
  • Used in astronomy to determine the composition of stars and galaxies
  • Used in forensic science to analyze evidence
• Atomic clocks: Highly accurate timekeeping devices based on the frequency of atomic transitions
  • Used in GPS navigation and telecommunications
• Nuclear energy: Harnessing the energy released from nuclear fission or fusion reactions
  • Nuclear power plants generate electricity
  • Radioisotopes used in medical imaging and cancer treatment
• Nanotechnology: Manipulation of matter at the atomic and molecular scale
  • Development of nanomaterials with unique properties (carbon nanotubes, graphene)
  • Targeted drug delivery and biosensors in medicine
• Quantum computing: Harnessing quantum phenomena (superposition and entanglement) to perform complex calculations
  • Potential applications in cryptography, optimization, and simulation of quantum systems