Atomic Structure

Atomic Structure

Protons, Neutrons, and Electrons

• Protons: positively charged particles that reside in the nucleus of an atom
  • Number of protons determines the element of an atom (atomic number)
  • Protons have a mass of approximately 1 atomic mass unit (amu)
• Neutrons: particles with no charge that reside in the nucleus of an atom
  • Number of neutrons can vary in an atom, leading to different isotopes of the same element
  • Neutrons have a mass of approximately 1 amu
• Electrons: negatively charged particles that orbit the nucleus of an atom
  • Number of electrons is equal to the number of protons in a neutral atom
  • Electrons have a negligible mass compared to protons and neutrons

Electron Configuration

• Electron shells: energy levels that electrons occupy around the nucleus
  • Each shell can hold a specific number of electrons (2, 8, 18, etc.)
• Electron spin: electrons can have a spin of +1/2 or -1/2, which determines their magnetic properties
• Pauli's Exclusion Principle: no two electrons in an atom can have the same set of quantum numbers (n, l, m, s)

Atomic Radius and Ionic Radius

• Atomic radius: distance from the nucleus to the outermost electron
  • Decreases from left to right across a period and increases from top to bottom in a group
• Ionic radius: distance from the nucleus to the outermost electron in an ion
  • Cations (positively charged ions) have smaller radii than anions (negatively charged ions)

Atomic Structure

• Protons are positively charged particles that reside in the nucleus of an atom and determine the element of an atom (atomic number).
• Protons have a mass of approximately 1 atomic mass unit (amu).

Neutrons

• Neutrons are particles with no charge that reside in the nucleus of an atom.
• The number of neutrons can vary in an atom, leading to different isotopes of the same element.
• Neutrons have a mass of approximately 1 amu.

Electrons

• Electrons are negatively charged particles that orbit the nucleus of an atom.
• The number of electrons is equal to the number of protons in a neutral atom.
• Electrons have a negligible mass compared to protons and neutrons.

Electron Configuration

Electron Shells

• Electron shells are energy levels that electrons occupy around the nucleus.
• Each shell can hold a specific number of electrons (2, 8, 18, etc.).

Electron Spin

• Electrons can have a spin of +1/2 or -1/2, which determines their magnetic properties.

Pauli's Exclusion Principle

• No two electrons in an atom can have the same set of quantum numbers (n, l, m, s).

Atomic Radius and Ionic Radius

Atomic Radius

• Atomic radius is the distance from the nucleus to the outermost electron.
• Atomic radius decreases from left to right across a period and increases from top to bottom in a group.

Ionic Radius

• Ionic radius is the distance from the nucleus to the outermost electron in an ion.
• Cations (positively charged ions) have smaller radii than anions (negatively charged ions).

Quantum Mechanics Key Principles

• Wave-particle duality is a fundamental property of particles, such as electrons, which can exhibit both wave-like and particle-like behavior.
• The uncertainty principle states that it is impossible to know certain properties, such as position and momentum, simultaneously with infinite precision.
• Quantum objects can exist in multiple states simultaneously, a phenomenon known as superposition.
• Entanglement occurs when the state of one particle is dependent on the state of another particle, even when separated by large distances.

Wave Functions and Probability

• A wave function (ψ) is a mathematical function that describes the quantum state of a system.
• Probability density (|ψ(x)|²) is the probability of finding a particle at a given location.
• Normalization is the process of ensuring the wave function is normalized to ensure the probability of finding the particle somewhere in space is 1.

Schrödinger Equation

• The Schrödinger equation is a mathematical equation that describes the time-evolution of a quantum system.
• The equation is written as: iℏ(∂ψ/∂t) = Hψ, where H is the Hamiltonian operator.
• The Schrödinger equation is used to determine the wave function ψ and energy eigenvalues of a system.

Operators and Measurements

• Operators are mathematical representations of physical observables, such as position, momentum, and energy.
• Measurement is the act of observing a quantum system, which collapses the wave function to an eigenstate of the measured operator.
• Eigenvalues and eigenvectors are the possible outcomes of a measurement, with the eigenvectors representing the possible states of the system.

Spin and Angular Momentum

• Spin is a fundamental property of particles, such as electrons and protons, that can be thought of as their intrinsic angular momentum.
• Angular momentum is a measure of an object's tendency to maintain its rotational motion.
• The spin-statistics theorem connects the spin of a particle to its statistical behavior (Bose-Einstein or Fermi-Dirac statistics).

Interference and Diffraction

• Interference is the combination of multiple waves, resulting in a new wave with an amplitude that depends on the relative phases of the individual waves.
• Diffraction is the bending of waves around obstacles or through narrow openings.
• The double-slit experiment is a classic demonstration of wave-particle duality and interference in quantum mechanics.