Atomic Physics

Study of atomic structure, electron configurations, and atomic spectra.

Definition

Atomic physics examines the structure of atoms, the arrangement of electrons around the nucleus, and the interaction of atoms with electromagnetic radiation. It bridges classical and quantum physics.

Key Concepts

mindmap
  root((Atomic Structure))
    Models
      Thomson Plum Pudding
      Rutherford Nuclear
      Bohr Quantized Orbits
      Quantum Mechanical Orbitals
    Quantum Numbers
      Principal n
      Orbital l
      Magnetic m_l
      Spin m_s
    Electron Configuration
      Shells K L M N
      Pauli Exclusion
      Aufbau Principle
    Spectra
      Emission Lines
      Absorption Lines
      Lyman Balmer Paschen
    Transitions
      Spontaneous Emission
      Stimulated Absorption
      Stimulated Emission
      LASER
  • Atomic Structure — nucleus (protons, neutrons) + electrons
  • Thomson Model — plum pudding model; discovery of the electron
  • Rutherford Model — nuclear atom, scattering experiments
  • Bohr Model — quantized electron orbits, angular momentum quantization
  • Bohr's Postulates — stationary states, $L=n\hbar$, photon emission during transitions
  • Energy Levels — discrete allowed energies for electrons
  • Quantum Numbers — $n$, $l$, $m_l$, $m_s$ describing electron states
  • Electron Shells — K, L, M, N... shells corresponding to $n = 1, 2, 3, 4...$
  • Atomic Spectra — emission and absorption line spectra
  • Spectral Series — Lyman (UV, $n \to 1$), Balmer (visible, $n \to 2$), Paschen (IR, $n \to 3$)
  • Rydberg Formula — wavelengths of spectral lines: $$\frac{1}{\lambda} = R_H\left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)$$
  • Ionization Energy — energy to remove an electron
  • Quantum Mechanical Model — Schrödinger orbitals, probability clouds, wave-particle duality
  • Pauli Exclusion Principle — no two electrons same quantum state
  • Stimulated Absorption — electron absorbs photon, excites to higher state
  • Spontaneous Emission — excited electron emits photon randomly ($\sim 10^{-8}$ s lifetime)
  • Stimulated Emission — incident photon triggers emission of an identical photon
  • LASER — Light Amplification by Stimulated Emission of Radiation; coherent, monochromatic, directional light
graph TB
    subgraph bohr["Bohr Model Energy Levels"]
        direction TB
        ion["Ionization<br/>E=0 eV"]
        n4["n=4<br/>-0.85 eV"]
        n3["n=3<br/>-1.51 eV"]
        n2["n=2<br/>-3.40 eV"]
        n1["n=1<br/>-13.6 eV<br/>Ground State"]
    end

    n1 -->|Absorb photon| n2
    n2 -->|Absorb photon| n3
    n2 -->|Emit photon<br/>Lyman UV| n1
    n3 -->|Emit photon<br/>Balmer Vis| n2
    n4 -->|Emit photon<br/>Paschen IR| n3
    n1 -->|Absorb photon<br/>Ionize| ion

    style n1 fill:#ffe3e3,stroke:#c92a2a
    style ion fill:#f8f9fa,stroke:#868e96,stroke-dasharray: 5 5

Key Formulas

Formula Description
$r_n = n^2 a_0 = (5.29 \times 10^{-11} \text{ m}),n^2$ Bohr orbit radius
$E_n = -\frac{13.6}{n^2}$ eV Hydrogen energy levels
$\frac{1}{\lambda} = R_H\left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)$ Rydberg formula
$L = n\hbar = r_n m v_n$ Quantized angular momentum
$\hbar = \frac{h}{2\pi} \approx 1.06 \times 10^{-34} \text{ J}\cdot\text{s}$ Reduced Planck constant
$hf = E_i - E_f$ Photon energy from transition
$E_{\text{ionization}} = 13.6$ eV Hydrogen ionization energy
$\mu = \frac{m_e M}{m_e + M}$ Reduced mass

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