Electromagnetic radiation interacts with matter in fascinating ways. From absorption and emission to scattering and reflection, these processes shape our world. Understanding these interactions is key to unlocking the power of spectroscopy and interpreting the information hidden in light.

Quantitative tools like the Beer-Lambert law and concepts like cross-section help us measure and analyze these interactions. Selection rules guide us in predicting allowed transitions, while quantum yield tells us how efficiently light energy is used. These principles form the foundation for spectroscopic techniques used across science and technology.

Interaction Processes

Absorption and Emission

• Absorption occurs when matter takes in electromagnetic radiation
  • Atoms or molecules absorb photons, increasing their energy state
  • Leads to electronic transitions, vibrational excitations, or rotational changes
• Emission involves the release of electromagnetic radiation by matter
  • Excited atoms or molecules return to lower energy states, emitting photons
  • Can be spontaneous or stimulated emission (basis for laser technology)
• Absorption and emission spectra are unique fingerprints for identifying substances
  • Flame tests utilize characteristic emission colors (sodium produces yellow flame)
  • Absorption spectroscopy detects specific wavelengths absorbed by samples

Scattering and Reflection

• Scattering redirects incident radiation in multiple directions
  • Elastic scattering maintains photon energy (Rayleigh scattering)
  • Inelastic scattering changes photon energy (Raman scattering)
  • Responsible for sky's blue color and sunset's red hue
• Reflection bounces radiation off a surface at a predictable angle
  • Specular reflection occurs on smooth surfaces (mirrors)
  • Diffuse reflection happens on rough surfaces (paper)
  • Follows the law of reflection: angle of incidence equals angle of reflection

Refraction and Transmittance

• Refraction bends light as it passes between media of different densities
  • Caused by change in light's speed when entering a new medium
  • Described by Snell's law: $n_1 \sin\theta_1 = n_2 \sin\theta_2$
  • Creates optical phenomena like mirages and rainbows
• Transmittance measures the fraction of radiation passing through a sample
  • Calculated as the ratio of transmitted to incident light intensity
  • Depends on material properties and thickness
  • Relates to absorbance: $T = 10^{-A}$, where T is transmittance and A is absorbance

Quantitative Descriptions

Beer-Lambert Law and Absorption

• Beer-Lambert law relates absorption to concentration and path length
  • Expressed as $A = \varepsilon bc$, where A is absorbance, ε is molar absorptivity, b is path length, and c is concentration
  • Allows quantitative analysis of solutions using spectrophotometry
  • Assumes monochromatic light and no interactions between absorbing species
• Absorbance defined as negative logarithm of transmittance
  • $A = -\log_{10}T = -\log_{10}(I/I_0)$, where I is transmitted intensity and I₀ is incident intensity
  • Additive for multiple absorbing species in a sample

Cross-section and Quantum Yield

• Cross-section quantifies probability of light-matter interactions
  • Measured in units of area (cm² or barns)
  • Larger cross-section indicates higher interaction probability
  • Varies with wavelength and type of interaction (absorption, scattering)
• Quantum yield measures efficiency of photochemical processes
  • Ratio of number of events to number of photons absorbed
  • Ranges from 0 to 1 for single-photon processes
  • Crucial in fluorescence spectroscopy and photochemistry
  • Calculated as $\Phi = \frac{\text{number of events}}{\text{number of photons absorbed}}$

Spectroscopic Rules

Selection Rules and Transition Probabilities

• Selection rules determine allowed spectroscopic transitions
  • Based on quantum mechanical principles and symmetry considerations
  • Govern changes in quantum numbers during transitions
  • Dipole selection rule: $\Delta l = \pm 1$ for electronic transitions
• Forbidden transitions have low probability but can still occur
  • Magnetic dipole and electric quadrupole transitions
  • Responsible for phenomena like phosphorescence
• Franck-Condon principle predicts transition intensities
  • Vertical transitions on potential energy surfaces
  • Explains vibrational fine structure in electronic spectra
• Spin selection rule: $\Delta S = 0$ for most transitions
  • Exceptions lead to intersystem crossing and phosphorescence