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Physical Chemistry I
Table of Contents
Unit 18 Overview: Spectroscopy in Physical Chemistry
18.1 Electromagnetic radiation and matter interaction
18.2 Rotational spectroscopy
18.3 Vibrational spectroscopy
18.4 Electronic spectroscopy
18.5 Nuclear magnetic resonance spectroscopy

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18.1 Electromagnetic radiation and matter interaction

Citation:

Electromagnetic radiation and matter interaction are key to understanding spectroscopy in physical chemistry. This topic covers how light waves interact with atoms and molecules, leading to absorption, emission, and scattering of photons.

We'll explore the properties of electromagnetic radiation, including wavelength and frequency. We'll also dive into how atoms and molecules absorb and emit radiation, and the different types of transitions that can occur during these interactions.

Properties of Electromagnetic Radiation

Fundamental Characteristics

  • Electromagnetic radiation consists of oscillating electric and magnetic fields that propagate through space at the speed of light
  • The electric and magnetic fields in electromagnetic radiation are perpendicular to each other and to the direction of propagation
  • Electromagnetic radiation can be characterized by its wavelength, frequency, and energy, which are related by the equation $E = hν$, where $E$ is energy, $h$ is Planck's constant, and $ν$ is frequency

Interaction with Matter

  • The interaction of electromagnetic radiation with matter can result in absorption, emission, or scattering of photons
    • Absorption occurs when the energy of the photon matches the energy difference between two allowed states of the atom or molecule
    • Emission occurs when an excited atom or molecule transitions from a higher energy state to a lower energy state, releasing a photon
    • Scattering involves the redirection of photons by matter without absorption or emission (Rayleigh scattering, Raman scattering)
  • The absorption and emission of electromagnetic radiation by matter are governed by the principles of quantum mechanics
    • Quantum mechanics describes the discrete nature of energy levels in atoms and molecules
    • Transitions between energy levels are subject to selection rules based on the conservation of energy and momentum

Absorption and Emission of Radiation

Absorption Process

  • Atoms and molecules can absorb electromagnetic radiation when the energy of the photon matches the energy difference between two allowed states of the atom or molecule
  • The absorption of a photon causes an electron to transition from a lower energy state to a higher energy state, resulting in an excited atom or molecule
    • The excited state is less stable and has a higher potential energy than the ground state
    • The lifetime of the excited state depends on the type of transition and the environment (typically on the order of nanoseconds to microseconds)

Emission Process

  • Excited atoms or molecules can emit electromagnetic radiation when the electron transitions from a higher energy state to a lower energy state, releasing a photon with energy equal to the difference between the two states
    • Emission can occur spontaneously or be stimulated by an external photon with the same energy
    • The emitted photon has the same frequency, phase, and direction as the stimulating photon in stimulated emission (basis for lasers)
  • The absorption and emission of electromagnetic radiation by atoms and molecules give rise to characteristic spectra that can be used to identify the composition of matter
    • Emission spectra consist of discrete wavelengths corresponding to the energy differences between allowed states
    • Absorption spectra show dark lines or bands where photons are absorbed by the sample
  • The intensity of the absorbed or emitted radiation depends on the population of atoms or molecules in the initial and final states, as described by the Boltzmann distribution
    • The Boltzmann distribution relates the population of states to the temperature and energy difference between the states
    • Higher temperature leads to a greater population of excited states and more intense emission

Frequency, Wavelength, and Energy

Relationship between Frequency and Wavelength

  • The frequency ($ν$) and wavelength ($λ$) of electromagnetic radiation are inversely related by the equation $c = λν$, where $c$ is the speed of light
    • Higher frequency corresponds to shorter wavelength, and lower frequency corresponds to longer wavelength
    • The speed of light in vacuum is approximately 3 × 10^8 m/s
  • The electromagnetic spectrum can be divided into different regions based on the frequency or wavelength of the radiation
    • Radio waves (low frequency, long wavelength)
    • Microwaves
    • Infrared
    • Visible light
    • Ultraviolet
    • X-rays
    • Gamma rays (high frequency, short wavelength)

Energy of Electromagnetic Radiation

  • The energy ($E$) of a photon is directly proportional to its frequency ($ν$) and inversely proportional to its wavelength ($λ$), as described by the equation $E = hν = hc/λ$, where $h$ is Planck's constant
    • Higher frequency (shorter wavelength) electromagnetic radiation has higher energy photons, while lower frequency (longer wavelength) radiation has lower energy photons
    • Planck's constant ($h$) is approximately 6.626 × 10^-34 J⋅s
  • The interaction of electromagnetic radiation with matter depends on the energy of the photons
    • Higher energy radiation (such as X-rays and gamma rays) is more penetrating and can potentially cause ionization
    • Lower energy radiation (such as radio waves and microwaves) is less penetrating and generally does not cause ionization

Transitions in Matter-Radiation Interactions

Electronic Transitions

  • Electronic transitions involve the excitation or de-excitation of electrons between different energy levels in atoms or molecules
    • Excitation occurs when an electron absorbs a photon and moves from a lower energy orbital to a higher energy orbital
    • De-excitation occurs when an electron emits a photon and moves from a higher energy orbital to a lower energy orbital
  • Electronic transitions typically result in the absorption or emission of ultraviolet or visible light
    • The energy differences between electronic states correspond to the energies of UV and visible photons
    • Examples of electronic transitions include the excitation of valence electrons in atoms and π-π* transitions in organic molecules

Vibrational Transitions

  • Vibrational transitions occur when the absorption of infrared radiation causes a change in the vibrational energy of a molecule
    • Molecules can vibrate in different modes, such as stretching or bending of the chemical bonds
    • The frequency of the vibration depends on the mass of the atoms and the strength of the bonds
  • Infrared spectroscopy is used to study vibrational transitions and provide information about the structure and functional groups of molecules
    • Different functional groups (C-H, O-H, C=O) have characteristic vibrational frequencies
    • The intensity of the absorption bands depends on the change in the dipole moment during the vibration

Rotational Transitions

  • Rotational transitions involve the absorption of microwave radiation, which causes a change in the rotational energy of a molecule
    • Molecules can rotate about different axes, depending on their moment of inertia
    • The energy differences between rotational states are typically smaller than those of vibrational and electronic states
  • Microwave spectroscopy is used to study rotational transitions and provide information about the geometry and bond lengths of molecules
    • The spacing between rotational energy levels depends on the moment of inertia of the molecule
    • Rotational spectra are sensitive to the presence of isotopes due to the change in mass and moment of inertia

Scattering and Luminescence

  • Raman scattering occurs when a photon interacts with a molecule and induces a change in the molecule's polarizability
    • The scattered photon has a different frequency than the incident photon, corresponding to the energy of a vibrational transition
    • Raman spectroscopy provides complementary information to infrared spectroscopy about the vibrational modes of molecules
  • Fluorescence and phosphorescence are processes in which a molecule absorbs a high-energy photon, transitions to an excited state, and then emits a lower-energy photon as it returns to the ground state
    • Fluorescence occurs rapidly (nanosecond timescale) and involves emission from a singlet excited state
    • Phosphorescence involves a delayed emission (milliseconds to seconds) due to a transition to a triplet state before returning to the ground state
    • These processes are used in various applications, such as fluorescence microscopy, chemical sensing, and organic light-emitting diodes (OLEDs)

Key Terms to Review (18)

Wave-particle duality: Wave-particle duality is the concept in quantum mechanics that describes how every particle or quantum entity, such as electrons and photons, exhibits both wave-like and particle-like properties. This fundamental principle challenges classical physics and is crucial for understanding various phenomena in physical chemistry.
Albert Einstein: Albert Einstein was a theoretical physicist best known for developing the theory of relativity, which revolutionized our understanding of space, time, and energy. His work established a framework for modern physics and laid the groundwork for concepts like wave-particle duality, the quantization of energy, and interactions between electromagnetic radiation and matter.
Quantum transitions: Quantum transitions refer to the changes in energy levels of a quantum system, typically observed in atoms and molecules when they absorb or emit electromagnetic radiation. These transitions occur when electrons move between discrete energy states, resulting in the absorption or release of photons. This phenomenon is crucial for understanding how matter interacts with electromagnetic radiation, impacting various processes such as spectroscopy and chemical reactions.
Nmr spectroscopy: NMR spectroscopy, or Nuclear Magnetic Resonance spectroscopy, is a powerful analytical technique used to determine the structure of organic compounds by observing the magnetic properties of atomic nuclei. It relies on the interaction between electromagnetic radiation and the nuclear spins of certain isotopes, primarily hydrogen-1 and carbon-13, allowing for the identification of molecular structures and dynamics.
Uv-vis spectroscopy: UV-Vis spectroscopy is an analytical technique that measures the absorption of ultraviolet and visible light by molecules in a sample. This technique allows for the investigation of electronic transitions in molecules, providing insights into their structure and concentration by analyzing how much light is absorbed at specific wavelengths.
Rayleigh Scattering: Rayleigh scattering is the elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the light. This phenomenon plays a critical role in how we perceive colors in the atmosphere, particularly explaining why the sky appears blue during the day and red during sunrise and sunset, connecting it to the interaction between electromagnetic radiation and matter.
Einstein's Photoelectric Equation: Einstein's photoelectric equation describes the relationship between the energy of incident light and the kinetic energy of emitted electrons when light hits a material. This equation is pivotal in understanding how electromagnetic radiation interacts with matter, specifically how photons can transfer energy to electrons and release them from a material's surface.
Absorption: Absorption refers to the process by which matter takes in electromagnetic radiation, converting it into internal energy, such as thermal energy or electronic excitations. This interaction is crucial for understanding how substances respond to light and other forms of electromagnetic radiation, influencing phenomena such as color perception and photochemistry.
Ultraviolet light: Ultraviolet light is a type of electromagnetic radiation with wavelengths shorter than visible light but longer than X-rays, typically ranging from about 10 nm to 400 nm. This form of radiation plays a crucial role in the interaction between electromagnetic radiation and matter, as it can excite electrons and lead to various chemical reactions and physical changes in materials.
Planck's Equation: Planck's Equation describes the relationship between the energy of a photon and its frequency, expressed as E = hν, where E is energy, h is Planck's constant, and ν (nu) is the frequency of the electromagnetic radiation. This equation is foundational in understanding how electromagnetic radiation interacts with matter, particularly in quantized energy levels and the emission or absorption of photons by atoms and molecules.
Photons: Photons are fundamental particles of light that carry electromagnetic energy and exhibit both wave-like and particle-like properties. They are the basic units of electromagnetic radiation, playing a crucial role in interactions between light and matter, which can result in phenomena such as absorption, emission, and scattering.
Infrared radiation: Infrared radiation is a type of electromagnetic radiation with wavelengths longer than visible light, typically ranging from about 700 nanometers to 1 millimeter. This form of radiation is crucial in various interactions with matter, as it can be absorbed or emitted by molecules, leading to changes in their vibrational and rotational states, which plays a significant role in molecular spectroscopy and thermal processes.
Beer-Lambert Law: The Beer-Lambert Law is a fundamental principle that describes the relationship between the absorption of light by a substance and its concentration in a solution. It states that the absorbance of light passing through a medium is directly proportional to the concentration of the absorbing species and the path length of the light. This law is crucial for understanding how electromagnetic radiation interacts with matter and forms the basis for various techniques in electronic spectroscopy.
Emission spectra: Emission spectra are the spectrum of light released from excited atoms or molecules as they return to lower energy states. When electrons in an atom absorb energy, they can jump to higher energy levels, and when they fall back to their original positions, they emit light at specific wavelengths, creating unique patterns of colors. These spectra serve as a fingerprint for elements, allowing scientists to identify substances and understand their properties.
Quantized energy levels: Quantized energy levels refer to the discrete energy states that particles, such as electrons, can occupy within an atom or a molecular system. These levels arise from the wave-like nature of particles, leading to the conclusion that only certain energy values are allowed, rather than a continuous range. This concept is fundamental in understanding how particles interact with electromagnetic radiation and play a crucial role in phenomena like absorption and emission spectra.
Energy quantization: Energy quantization refers to the concept that energy exists in discrete units rather than a continuous range. This idea is foundational in quantum mechanics, where particles, such as electrons, can only occupy specific energy levels. The quantized nature of energy leads to various phenomena, including the discrete spectra observed in atoms and molecules, as well as influencing how systems interact with electromagnetic radiation.
Excited states: Excited states refer to the higher energy levels of an atom or molecule, which occur when electrons absorb energy and move to a state beyond their ground state. These states are temporary and play a crucial role in interactions with electromagnetic radiation, leading to phenomena like absorption spectra and photochemical reactions.
Max Planck: Max Planck was a German physicist who is best known for his role in the development of quantum theory, which fundamentally changed our understanding of atomic and subatomic processes. His introduction of the concept of quantization of energy paved the way for various principles and models that explain the behavior of particles and their interactions with electromagnetic radiation.