🌈Spectroscopy Unit 1 – Spectroscopy: Intro to EM Radiation

Key Concepts and Definitions

• Spectroscopy involves the study of the interaction between matter and electromagnetic radiation
• Electromagnetic radiation consists of oscillating electric and magnetic fields that propagate through space at the speed of light
• Wavelength ($\lambda$) represents the distance between two consecutive peaks or troughs of an electromagnetic wave
• Frequency ($\nu$) refers to the number of wave cycles that pass a fixed point in space per unit time
• Energy of a photon ($E$) is directly proportional to its frequency and inversely proportional to its wavelength, as described by the equation $E = h\nu = hc/\lambda$, where $h$ is Planck's constant and $c$ is the speed of light
  • Higher frequency and shorter wavelength correspond to higher energy photons
  • Lower frequency and longer wavelength correspond to lower energy photons
• Absorption occurs when a substance takes in electromagnetic radiation, causing its atoms or molecules to transition to higher energy states
• Emission happens when a substance releases electromagnetic radiation, as its atoms or molecules transition from higher to lower energy states

Electromagnetic Spectrum Basics

• The electromagnetic spectrum encompasses all possible frequencies and wavelengths of electromagnetic radiation
• It ranges from low-frequency, long-wavelength radio waves to high-frequency, short-wavelength gamma rays
• The visible light spectrum, which humans can perceive, is only a small portion of the entire electromagnetic spectrum (wavelengths between 380 and 700 nm)
• Different regions of the electromagnetic spectrum have distinct properties and interact with matter in various ways
  • Radio waves have the longest wavelengths and lowest frequencies, while gamma rays have the shortest wavelengths and highest frequencies
  • Microwaves, infrared radiation, visible light, ultraviolet radiation, and X-rays lie between these two extremes
• The relationship between wavelength and frequency is given by the equation $c = \lambda\nu$, where $c$ is the speed of light
• The energy of electromagnetic radiation increases as the frequency increases and the wavelength decreases

Types of EM Radiation

• Radio waves have wavelengths longer than 1 mm and are used in radio and television broadcasting, cellular communication, and radar systems
• Microwaves have wavelengths between 1 mm and 1 m and are used in microwave ovens, satellite communication, and radar technology
• Infrared radiation has wavelengths between 700 nm and 1 mm and is associated with heat emission from objects
  • Near-infrared (NIR) radiation (700 nm to 2.5 μm) is used in remote sensing and fiber-optic communication
  • Mid-infrared (MIR) radiation (2.5 μm to 25 μm) is used in thermal imaging and chemical analysis
  • Far-infrared (FIR) radiation (25 μm to 1 mm) is used in astronomical observations and material science
• Visible light has wavelengths between 380 and 700 nm and is the only portion of the electromagnetic spectrum that humans can perceive
  • Different wavelengths of visible light correspond to different colors (red, orange, yellow, green, blue, indigo, and violet)
• Ultraviolet (UV) radiation has wavelengths between 10 and 380 nm and is responsible for sunburns and the production of vitamin D in the skin
  • UV-A (315-400 nm) is used in black lights and tanning beds
  • UV-B (280-315 nm) causes sunburns and is partially absorbed by the Earth's ozone layer
  • UV-C (100-280 nm) is the most energetic and is completely absorbed by the Earth's atmosphere
• X-rays have wavelengths between 0.01 and 10 nm and are used in medical imaging, airport security scanners, and crystallography
• Gamma rays have wavelengths shorter than 0.01 nm and are produced by radioactive decay and cosmic sources

Interaction of EM Radiation with Matter

• When electromagnetic radiation interacts with matter, it can be absorbed, transmitted, reflected, or scattered
• Absorption occurs when the energy of the photon matches the energy difference between two quantum states of an atom or molecule
  • The absorbed energy can cause electronic, vibrational, or rotational transitions, depending on the wavelength of the radiation
  • Absorption spectra show dark lines or bands corresponding to the specific wavelengths absorbed by the substance
• Transmission happens when electromagnetic radiation passes through a substance without being absorbed
  • The degree of transmission depends on the material's properties and the wavelength of the radiation
• Reflection occurs when electromagnetic radiation bounces off a surface, with the angle of incidence equal to the angle of reflection
  • Specular reflection (mirrors) occurs when the surface is smooth and flat
  • Diffuse reflection (matte surfaces) occurs when the surface is rough or irregular
• Scattering involves the redirection of electromagnetic radiation in multiple directions due to interactions with particles or inhomogeneities in the medium
  • Rayleigh scattering (blue sky) occurs when the particles are much smaller than the wavelength of the radiation
  • Mie scattering (white clouds) occurs when the particles are comparable in size to the wavelength of the radiation

Spectroscopic Techniques and Instrumentation

• Spectroscopic techniques involve the use of instruments to measure the interaction of electromagnetic radiation with matter
• UV-Visible spectroscopy measures the absorption or transmission of UV and visible light by a sample
  • It is used to determine the concentration of absorbing species in solution using the Beer-Lambert law, $A = \epsilon bc$, where $A$ is absorbance, $\epsilon$ is the molar attenuation coefficient, $b$ is the path length, and $c$ is the concentration
• Infrared (IR) spectroscopy measures the absorption of infrared radiation by a sample
  • It provides information about the presence of specific functional groups and molecular structure
  • Fourier-transform infrared (FTIR) spectroscopy is a common technique that uses an interferometer to collect high-resolution data over a wide spectral range
• Raman spectroscopy measures the inelastic scattering of monochromatic light by a sample
  • It provides information about the vibrational and rotational modes of molecules
  • Raman spectroscopy is complementary to IR spectroscopy and is particularly useful for studying symmetric molecules and non-polar bonds
• Atomic absorption spectroscopy (AAS) measures the absorption of light by free atoms in the gaseous state
  • It is used for the quantitative determination of elemental composition in a sample
• X-ray spectroscopy techniques, such as X-ray fluorescence (XRF) and X-ray diffraction (XRD), use X-rays to probe the elemental composition and crystal structure of materials

Applications in Chemistry and Physics

• Spectroscopy is used to identify and quantify chemical compounds based on their unique absorption or emission spectra
  • Different functional groups and molecular structures have characteristic spectral features that can be used for identification
  • The concentration of a substance can be determined using the Beer-Lambert law and UV-Visible spectroscopy
• Spectroscopic techniques are employed to study reaction kinetics and mechanisms by monitoring the appearance or disappearance of specific spectral features over time
• Spectroscopy plays a crucial role in environmental monitoring and analysis
  • IR and Raman spectroscopy can detect and quantify pollutants, such as greenhouse gases and organic contaminants
  • AAS and XRF are used to measure the concentration of heavy metals in soil and water samples
• In astronomy, spectroscopy is used to determine the composition, temperature, and velocity of celestial objects
  • The Doppler shift of spectral lines provides information about the motion of stars and galaxies
  • The presence of specific absorption or emission lines indicates the presence of certain elements or molecules in stellar atmospheres or interstellar clouds
• Spectroscopy is essential in the development and characterization of new materials
  • IR and Raman spectroscopy can probe the chemical structure and bonding in polymers, composites, and nanomaterials
  • XRD is used to determine the crystal structure and phase composition of materials

Mathematical Models and Equations

• The Beer-Lambert law, $A = \epsilon bc$, relates the absorbance of a sample to its concentration and the path length of the light
  • $A$ is the absorbance, $\epsilon$ is the molar attenuation coefficient (a constant for a given substance at a specific wavelength), $b$ is the path length, and $c$ is the concentration
• The Rydberg equation, $1/\lambda = R(1/n_1^2 - 1/n_2^2)$, describes the wavelengths of light emitted or absorbed by hydrogen-like atoms
  • $\lambda$ is the wavelength, $R$ is the Rydberg constant, and $n_1$ and $n_2$ are the principal quantum numbers of the initial and final states, respectively
• The Schrödinger equation, $\hat{H}\Psi = E\Psi$, is a fundamental equation in quantum mechanics that describes the energy states of a system
  • $\hat{H}$ is the Hamiltonian operator, $\Psi$ is the wavefunction, and $E$ is the energy of the system
  • The solutions to the Schrödinger equation give the allowed energy levels and wavefunctions for a given system, which are related to the observed spectroscopic transitions
• The Franck-Condon principle states that electronic transitions in molecules occur on a much faster timescale than nuclear motion
  • This leads to the formation of vibrational progressions in electronic spectra, where the intensity of each vibrational band is proportional to the overlap of the initial and final vibrational wavefunctions
• The selection rules determine which transitions between energy levels are allowed or forbidden based on the symmetry and angular momentum of the states involved
  • For example, in IR spectroscopy, only transitions that result in a change in the dipole moment of the molecule are allowed

Practical Examples and Problem Solving

• In a UV-Visible spectroscopy experiment, a student measures the absorbance of a 1.5 × 10⁻⁵ M solution of an organic dye at 520 nm. The path length of the cuvette is 1 cm, and the molar attenuation coefficient of the dye at this wavelength is 2.0 × 10⁴ M⁻¹cm⁻¹. Calculate the expected absorbance of the solution.
  • Using the Beer-Lambert law, $A = \epsilon bc$, we have:
    • $\epsilon = 2.0 \times 10^4 \text{ M}^{-1}\text{cm}^{-1}$
    • $b = 1 \text{ cm}$
    • $c = 1.5 \times 10^{-5} \text{ M}$
  • Substituting these values, we get: $A = (2.0 \times 10^4 \text{ M}^{-1}\text{cm}^{-1})(1 \text{ cm})(1.5 \times 10^{-5} \text{ M}) = 0.30$
  • Therefore, the expected absorbance of the solution is 0.30.
• A chemist is analyzing a mixture of two compounds using IR spectroscopy. The first compound has a strong absorption peak at 1720 cm⁻¹, while the second compound has a strong absorption peak at 2220 cm⁻¹. Identify the likely functional groups present in each compound.
  • The absorption peak at 1720 cm⁻¹ is characteristic of the C=O stretching vibration in carbonyl compounds, such as aldehydes, ketones, esters, and carboxylic acids
  • The absorption peak at 2220 cm⁻¹ is characteristic of the C≡N stretching vibration in nitriles
  • Therefore, the first compound likely contains a carbonyl group, while the second compound likely contains a nitrile group
• An astronomer observes the emission spectrum of a distant star and notices a series of lines in the visible region that correspond to the Balmer series of hydrogen. The wavelengths of these lines are measured to be slightly shorter than the expected values for hydrogen in the laboratory. Explain the reason for this observation and what it implies about the star's motion.
  • The observed wavelengths of the Balmer series lines are shorter than the expected values, which indicates a blueshift in the spectrum
  • A blueshift occurs when the source of light is moving towards the observer, causing the wavelengths to be compressed due to the Doppler effect
  • In this case, the blueshift implies that the star is moving towards the Earth at a significant velocity
  • The magnitude of the blueshift can be used to calculate the radial velocity of the star using the Doppler shift formula, $\Delta \lambda / \lambda = v / c$, where $\Delta \lambda$ is the change in wavelength, $\lambda$ is the original wavelength, $v$ is the radial velocity, and $c$ is the speed of light