⚛️Atomic Physics Unit 5 – Spectroscopy and Transitions

Key Concepts and Principles

• Spectroscopy studies the interaction between matter and electromagnetic radiation
• Atoms absorb and emit photons of specific energies corresponding to transitions between energy levels
• Energy levels in atoms are quantized and determined by the electronic configuration
• Transitions between energy levels give rise to characteristic spectral lines
• Selection rules govern the allowed transitions based on quantum numbers and symmetry considerations
• Spectral lines can be classified into series (Lyman, Balmer, Paschen) based on the final energy level
• The wavelength and frequency of spectral lines are related by the equation $\lambda = c/f$
• The energy of a photon is given by $E = hf$, where $h$ is Planck's constant

Atomic Energy Levels

• Atoms have discrete energy levels determined by the arrangement of electrons in orbitals
• The energy levels are labeled by principal quantum number $n$ (1, 2, 3, ...)
• Sublevels are characterized by the orbital angular momentum quantum number $l$ (s, p, d, f)
• Energy levels are split into sublevels due to electron-electron interactions and spin-orbit coupling
• The ground state is the lowest energy level, while excited states have higher energies
• Electrons can transition between energy levels by absorbing or emitting photons
• The energy difference between levels determines the wavelength of the associated spectral line
• The Rydberg formula relates the wavelength of spectral lines to the energy levels involved in the transition

Types of Spectroscopy

• Emission spectroscopy analyzes the light emitted by atoms or molecules in excited states
  • Atoms are excited by heat, electrical discharge, or laser pulses
  • Examples include flame emission and inductively coupled plasma (ICP) spectroscopy
• Absorption spectroscopy measures the absorption of light as it passes through a sample
  • Atoms or molecules absorb photons and transition to higher energy levels
  • Examples include atomic absorption spectroscopy (AAS) and UV-visible spectroscopy
• Fluorescence spectroscopy studies the emission of light from atoms or molecules after excitation
  • Excited states relax back to the ground state by emitting photons
  • Fluorescence is used in biological and chemical sensing applications
• Raman spectroscopy probes the vibrational and rotational modes of molecules
  • Inelastic scattering of light by molecules provides information about their structure and composition

Transition Rules and Selection

• Selection rules determine the allowed transitions between energy levels
• Electric dipole transitions are the most common and follow specific rules
  • The change in orbital angular momentum $\Delta l = \pm 1$
  • The change in spin $\Delta s = 0$
  • The change in total angular momentum $\Delta j = 0, \pm 1$ (except $j = 0 \to j = 0$)
• Magnetic dipole and electric quadrupole transitions have different selection rules
• Parity selection rule: the parity of the initial and final states must change for allowed transitions
• Laporte selection rule: transitions between states of the same parity are forbidden in centrosymmetric systems
• Spin selection rule: transitions between states with different spin multiplicities are forbidden

Spectral Lines and Series

• Spectral lines arise from transitions between specific energy levels in atoms
• Lines are characterized by their wavelength, intensity, and shape (broadening mechanisms)
• Spectral series are groups of lines corresponding to transitions to a common lower energy level
  • Lyman series: transitions to the ground state ($n = 1$) in hydrogen
  • Balmer series: transitions to the first excited state ($n = 2$) in hydrogen
  • Paschen series: transitions to the second excited state ($n = 3$) in hydrogen
• Fine structure splitting of spectral lines occurs due to spin-orbit coupling and relativistic effects
• Hyperfine structure splitting arises from the interaction between the electron and nuclear spins
• The intensity of spectral lines depends on the population of the energy levels and transition probabilities

Instrumentation and Techniques

• Spectrometers are instruments used to measure and analyze spectra
  • Components include light sources, sample holders, dispersive elements (prisms, gratings), and detectors
• Monochromators select a narrow range of wavelengths for analysis
  • Gratings or prisms disperse light, and slits control the bandwidth
• Detectors convert light into electrical signals for quantitative analysis
  • Examples include photomultiplier tubes (PMTs), charge-coupled devices (CCDs), and photodiodes
• Fourier transform spectroscopy uses interferometry to obtain high-resolution spectra
  • Michelson interferometer splits and recombines light, creating an interferogram
  • Fourier transform of the interferogram yields the spectrum
• Laser spectroscopy techniques offer high sensitivity and selectivity
  • Examples include laser-induced fluorescence (LIF) and cavity ring-down spectroscopy (CRDS)

Applications in Research and Industry

• Elemental analysis: identifying and quantifying elements in samples
  • Atomic absorption spectroscopy (AAS) for trace metal analysis
  • Inductively coupled plasma (ICP) spectroscopy for multi-element analysis
• Environmental monitoring: detecting pollutants and contaminants in air, water, and soil
  • Measuring heavy metals, pesticides, and organic compounds
• Astrophysics: studying the composition and properties of celestial objects
  • Stellar spectroscopy reveals temperature, composition, and velocity of stars
  • Spectroscopy of galaxies and interstellar medium provides insights into the universe
• Plasma diagnostics: characterizing the properties of plasmas in fusion reactors and industrial processes
  • Measuring electron temperature, density, and impurity concentrations
• Biomedical applications: analyzing biological samples and developing diagnostic tools
  • Fluorescence spectroscopy for studying protein structure and interactions
  • Raman spectroscopy for non-invasive tissue analysis and cancer detection

Problem-Solving and Calculations

• Calculating the wavelength or frequency of spectral lines using the Rydberg formula
  • $1/\lambda = R_H (1/n_1^2 - 1/n_2^2)$, where $R_H$ is the Rydberg constant and $n_1$, $n_2$ are the principal quantum numbers
• Determining the energy levels and transitions involved in observed spectral lines
• Estimating the population of energy levels using the Boltzmann distribution
  • $N_i/N_j = (g_i/g_j) \exp[-(E_i - E_j)/kT]$, where $N_i$, $N_j$ are the populations, $g_i$, $g_j$ are the degeneracies, and $E_i$, $E_j$ are the energies of levels $i$ and $j$
• Calculating the intensity of spectral lines based on transition probabilities and level populations
• Interpreting and analyzing experimental spectra to extract information about atomic and molecular systems
• Applying selection rules to determine allowed and forbidden transitions
• Using spectroscopic data to determine fundamental constants (e.g., Rydberg constant, fine structure constant)