5.1 Principles of electromagnetic radiation and interaction with matter

Electromagnetic radiation is the backbone of spectroscopic methods. From radio waves to gamma rays, different types of radiation interact uniquely with matter, causing absorption, emission, or scattering. These interactions form the basis for various analytical techniques.

The relationship between energy, frequency, and wavelength is key to understanding how radiation behaves. The Beer-Lambert law, which relates light absorption to sample properties, is crucial for quantitative analysis in spectroscopy. It's widely used but has limitations to consider.

Electromagnetic Spectrum and its Properties

Regions of the Electromagnetic Spectrum

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• The electromagnetic spectrum is the range of all possible frequencies or wavelengths of electromagnetic radiation, from low-frequency radio waves to high-frequency gamma rays
• The electromagnetic spectrum is divided into different regions based on their wavelengths and frequencies:
  • Radio waves (longest wavelength, lowest frequency)
  • Microwaves
  • Infrared
  • Visible light
  • Ultraviolet
  • X-rays
  • Gamma rays (shortest wavelength, highest frequency)

Properties and Interactions of Electromagnetic Radiation

• Different regions of the electromagnetic spectrum have unique properties and interact with matter differently
  • Ability to penetrate materials (radio waves can penetrate walls, while visible light cannot)
  • Cause ionization (high-energy X-rays and gamma rays can ionize atoms)
  • Be absorbed by specific substances (infrared radiation is absorbed by water and carbon dioxide)
• The energy of electromagnetic radiation increases with increasing frequency and decreasing wavelength, which affects how it interacts with matter
  • Higher energy radiation (ultraviolet, X-rays, gamma rays) can cause more significant changes in matter, such as ionization or chemical reactions
  • Lower energy radiation (radio waves, microwaves, infrared) tends to cause less dramatic effects, such as heating or inducing molecular vibrations

Absorption, Emission, and Scattering of Radiation

Absorption of Electromagnetic Radiation

• Absorption occurs when electromagnetic radiation is taken up by matter, causing the atoms or molecules to transition to higher energy states or vibrate more vigorously
• The absorption of electromagnetic radiation by matter is selective, depending on the frequency of the radiation and the structure of the atoms or molecules
  • Atoms absorb specific frequencies of light that correspond to the energy differences between their electronic states
  • Molecules absorb specific frequencies of light that correspond to the energy differences between their vibrational and rotational states

Emission of Electromagnetic Radiation

• Emission is the process by which matter releases electromagnetic radiation, often as a result of electrons transitioning from higher to lower energy states
• Emission spectra can be continuous or discrete:
  • Continuous emission spectra (blackbody radiation from hot objects like stars or heated metal)
  • Discrete emission spectra (atomic emission spectra from excited atoms or molecular emission spectra from excited molecules)
• The frequency and wavelength of the emitted radiation depend on the energy differences between the initial and final states of the atoms or molecules

Scattering of Electromagnetic Radiation

• Scattering is the process by which electromagnetic radiation is deflected or redirected by matter, without being absorbed or emitted
• Scattering can be elastic or inelastic:
  • Elastic scattering (Rayleigh scattering): the energy of the scattered radiation is the same as the incident radiation (blue sky due to scattering of sunlight by air molecules)
  • Inelastic scattering (Raman scattering): the energy of the scattered radiation is different from the incident radiation due to energy transfer between the radiation and the matter (used in Raman spectroscopy to study molecular vibrations)

Energy, Frequency, and Wavelength Relationship

• The energy of a photon (a quantum of electromagnetic radiation) is directly proportional to its frequency and inversely proportional to its wavelength, as described by the Planck-Einstein relation: $E = hν = hc/λ$
  • $E$ is the energy of the photon
  • $h$ is Planck's constant ($6.626 × 10^{-34}$ J⋅s)
  • $ν$ is the frequency of the radiation
  • $c$ is the speed of light in vacuum ($2.998 × 10^8$ m/s)
  • $λ$ is the wavelength of the radiation
• Higher frequency and shorter wavelength electromagnetic radiation has higher energy, while lower frequency and longer wavelength radiation has lower energy
  • Gamma rays and X-rays have high frequencies, short wavelengths, and high energies
  • Radio waves and microwaves have low frequencies, long wavelengths, and low energies
• The relationship between energy, frequency, and wavelength is fundamental to understanding the properties and interactions of electromagnetic radiation with matter
  • The energy of the radiation determines the types of transitions or changes it can induce in atoms or molecules (electronic, vibrational, or rotational)
  • The frequency and wavelength of the radiation determine its region in the electromagnetic spectrum and its interaction with matter (absorption, emission, or scattering)

Beer-Lambert Law and Applications

Principles of the Beer-Lambert Law

• The Beer-Lambert law (also known as Beer's law) relates the attenuation of light to the properties of the material through which the light is traveling
• The law states that the absorbance of a solution is directly proportional to:
  • The concentration of the absorbing species in the solution
  • The path length of the sample
• Mathematically, the Beer-Lambert law is expressed as $A = εbc$
  • $A$ is the absorbance
  • $ε$ is the molar attenuation coefficient (a measure of how strongly a substance absorbs light at a particular wavelength)
  • $b$ is the path length (the distance the light travels through the sample)
  • $c$ is the concentration of the absorbing species

Applications and Limitations of the Beer-Lambert Law

• The Beer-Lambert law is the basis for quantitative spectroscopic analysis, allowing the determination of the concentration of an absorbing species in a solution by measuring its absorbance
  • A calibration curve is created by measuring the absorbance of standard solutions with known concentrations
  • The concentration of an unknown sample can be determined by comparing its absorbance to the calibration curve
• Deviations from the Beer-Lambert law can occur due to various factors:
  • High concentrations of the absorbing species (leading to nonlinear relationship between absorbance and concentration)
  • Non-monochromatic light sources (the law assumes monochromatic light)
  • Presence of other absorbing or scattering species in the sample (interfering with the absorbance measurement)
• The law is widely applied in various analytical techniques for the quantitative determination of analytes in various matrices:
  • UV-visible spectroscopy (determining the concentration of colored compounds or metal complexes)
  • Infrared spectroscopy (quantifying the concentration of organic compounds or functional groups)
  • Atomic absorption spectroscopy (measuring the concentration of metal ions in solution)