In Depth Notes on Atomic Physics

Atomic Physics Overview

  • Classical Physics (Before 1900)

    • Focused on macroscopic phenomena.
    • Examples: cannon balls, planets, wave motion, sound, optics, and electromagnetism.

  • Modern Physics (After 1900)

    • Concerned with microscopic world, especially subatomic particles.

Historical Perspectives on Matter

  • Greek Philosophers (400 B.C.)

    • Debated whether matter is continuous or discrete.
    • Continuous: can be divided indefinitely.
    • Discrete: consists of ultimate indivisible particles.
    • Majority, including Aristotle, favored continuous theory.

  • John Dalton (1807)

    • Proposed matter is discrete as particles (atoms).
    • Each element has identical atoms distinct from other elements.
    • Visualized atoms as featureless spheres of uniform density.
Dalton's Atomic Models
  • Billiard Ball Model (1807)
    • Atoms depicted as tiny, indivisible, uniformly dense spheres.

Discoveries in Atomic Structure

  • J.J. Thomson (1903)

    • Discovered electrons using cathode-ray tubes.
    • Found mass of electron: 9.11×10−31 kg9.11 \times 10^{-31} \text{ kg}
    • Charge of electron: −1.60×10−19 C-1.60 \times 10^{-19} \text{ C}
    • Created the Plum Pudding Model where electrons are embedded in a positive mass.

  • Ernest Rutherford (1911)

    • Conducted the Gold Foil Experiment which revealed:

    • Most of the atom is empty space.

    • Presence of a dense, positively charged nucleus (protons).

    • Developed the Nuclear Model.

    • Rutherford’s Findings:

    • Alpha particles mostly went through gold foil, confirming empty space.

    • Only some particles ricocheted back, indicating a small, dense nucleus.

The Bohr Model

  • Niels Bohr proposed that electrons travel in definite orbits around the nucleus.

    • Defined these orbits with principal quantum numbers nn, representing distinct energy levels.
    • Ground state: n=1n=1; Excited states: n=2,3,4n=2, 3, 4, etc.

  • Energy Levels

    • Total energy given by: En=−13.60n2 eVE_n = -\frac{13.60}{n^2} \text{ eV}
    • Binding energy decreases with increasing nn.
    • Pictorially, energy levels are not evenly spaced and have significance for atomic behavior.

Quantum Physics Foundations

  • Planck’s Quantum Hypothesis (1900)

    • Introduced the idea of quantized energy: E=hfE = hf (where hh is Planck's constant).

  • Photoelectric Effect

    • Photons can cause the emission of electrons when exposed to light, demonstrating the particle nature of light.

Wave-Particle Duality

  • Light Behavior:
    • Demonstrates wave-like properties (interference, diffraction) and particle-like properties (photons).
  • De Broglie's Hypothesis (1925)
    • Proposed that all matter has wave properties: λ=hmv\lambda = \frac{h}{mv} where λ\lambda is wavelength, mm is mass, and vv is velocity.

Quantum Mechanics and Schrödinger's Model

  • Heisenberg’s Uncertainty Principle (1927)
    • States it's impossible to precisely know both position and momentum of a particle simultaneously.
  • Schrödinger’s Wave Equation (1926)
    • Focuses on the wave nature of electrons.
    • Determines the probability distribution of an electron around the nucleus (electron cloud model).

Key Formulas and Concepts

  • Photon Energy: E=hfE = hf
  • Hydrogen Electron Radii: rn=0.053n2 nmr_n = 0.053n^2 \text{ nm}
  • Hydrogen Electron Energy Levels: En=−13.60n2 eVE_n = -\frac{13.60}{n^2} \text{ eV}
  • De Broglie Wavelength: λ=hmv\lambda = \frac{h}{mv}