Glossary

7.1 Electromagnetic spectrum and molecular energy levels

4 min read•july 30, 2024

The electromagnetic spectrum spans from low-energy radio waves to high-energy gamma rays. It's crucial for understanding molecular transitions, as different regions correspond to specific energy changes in molecules, like rotations, vibrations, and electronic shifts.

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Molecules have discrete energy levels that can be probed using spectroscopy. When a molecule absorbs or emits a photon, it transitions between these levels. The energy difference determines which part of the spectrum is involved, linking molecular structure to spectroscopic observations.

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Electromagnetic Spectrum and Molecular Energy

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Electromagnetic Radiation Characteristics

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  • The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation, from low-frequency radio waves to high-frequency gamma rays
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  • Electromagnetic radiation can be described as a wave with a specific wavelength, frequency, and energy, related by the equation E=hνE = hν, where EE is energy, hh is , and νν is frequency
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  • The energy of a photon determines the region of the electromagnetic spectrum involved in a molecular transition (microwave, infrared, visible, or ultraviolet)
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Molecular Energy Levels and Transitions

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  • Molecules have discrete, quantized energy levels that correspond to different electronic, vibrational, and rotational states
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  • Transitions between these energy levels can occur when a molecule absorbs or emits a photon with an energy that matches the energy difference between the levels
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1. [Absorption](https://www.fiveableKeyTerm:absorption): molecule absorbs a photon and transitions to a higher energy level
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2. [Emission](https://www.fiveableKeyTerm:Emission): molecule emits a photon and transitions to a lower energy level
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Regions of the Electromagnetic Spectrum

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Low Energy Regions

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  • The microwave region corresponds to transitions between in molecules
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- Wavelengths between 1 mm and 1 m
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- Example: microwave spectroscopy used to study molecular rotations
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  • The infrared region corresponds to transitions between in molecules
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- Wavelengths between 700 nm and 1 mm
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- Example: IR spectroscopy used to identify functional groups in organic molecules
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High Energy Regions

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  • The visible region corresponds to transitions between electronic energy levels in molecules
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- Wavelengths between 400 and 700 nm
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- Example: visible absorption spectroscopy used to study electronic transitions in conjugated systems
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  • The ultraviolet region also corresponds to transitions between electronic energy levels, but with higher energies and shorter wavelengths than the visible region
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- Wavelengths between 10-400 nm
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- Example: UV-Vis spectroscopy used to study electronic transitions in aromatic compounds
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  • X-rays and gamma rays have the highest energies and shortest wavelengths
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- Can cause ionization or nuclear transitions in molecules
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- Example: X-ray crystallography used to determine molecular structures
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Quantized Energy Levels in Molecules

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Origin and Characterization of Quantized Energy Levels

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  • Molecules have discrete, quantized energy levels that arise from the allowed solutions to the Schrödinger equation for the molecular system
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  • The quantized energy levels are characterized by quantum numbers that describe the electronic, vibrational, and rotational states of the molecule
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- Electronic quantum numbers (n, l, ml, ms) describe the energy, shape, and orientation of molecular orbitals
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- Vibrational quantum numbers (v) describe the vibrational modes and energy levels of the molecule
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- Rotational quantum numbers (J, K, M) describe the rotational energy levels and angular momentum of the molecule
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Spectroscopic Applications

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  • The energy differences between these quantized levels determine the wavelengths of light that can be absorbed or emitted by the molecule
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  • Spectroscopy techniques probe these energy level differences to obtain information about the structure and properties of molecules
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1. Absorption spectroscopy: measures the wavelengths of light absorbed by a molecule
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2. Emission spectroscopy: measures the wavelengths of light emitted by a molecule
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3. [Raman spectroscopy](https://www.fiveableKeyTerm:Raman_spectroscopy): measures the wavelengths of light scattered by a molecule
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  • The selection rules, based on the symmetry and allowed transitions between energy levels, govern which spectroscopic transitions are possible for a given molecule
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- Example: in a centrosymmetric molecule, transitions between energy levels with the same parity are forbidden
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Photon Energy vs Frequency and Wavelength

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Energy-Frequency Relationship

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  • The energy of a photon is directly proportional to its frequency, as described by the equation E=hνE = hν, where EE is energy, hh is Planck's constant, and νν is frequency
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  • Higher frequency photons have higher energies, while lower frequency photons have lower energies
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  • The relationship between photon energy and frequency is linear, with the slope determined by Planck's constant
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- Example: a photon with a frequency of $6 \times 10^{14}$ Hz has twice the energy of a photon with a frequency of $3 \times 10^{14}$ Hz
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Energy-Wavelength Relationship

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  • The energy of a photon is inversely proportional to its wavelength, as described by the equation E=hc/λE = hc/λ, where EE is energy, hh is Planck's constant, cc is the , and λλ is wavelength
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  • Shorter wavelength photons have higher energies, while longer wavelength photons have lower energies
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  • The relationship between photon energy and wavelength is hyperbolic, with energy approaching infinity as wavelength approaches zero
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- Example: a photon with a wavelength of 500 nm has twice the energy of a photon with a wavelength of 1000 nm
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  • Understanding these relationships is crucial for interpreting molecular spectra and determining the energy levels involved in molecular transitions

Key Terms to Review (18)

Absorption: Absorption is the process by which molecules take in energy from electromagnetic radiation, leading to an increase in their energy levels. This process occurs when the energy of the incoming radiation matches the energy difference between molecular states, allowing for transitions between various energy levels, including electronic, vibrational, and rotational states. The ability of molecules to absorb specific wavelengths of light is crucial for understanding how they interact with their environment and is foundational in areas like spectroscopy and photochemistry.
Electronvolt: An electronvolt is a unit of energy that is commonly used in the fields of physics and chemistry, particularly in the context of atomic and molecular processes. It is defined as the amount of kinetic energy gained by a single electron when it is accelerated through an electric potential difference of one volt. This unit provides a convenient way to express energy levels in atoms and molecules, particularly when discussing electronic transitions and interactions with electromagnetic radiation.
Emission: Emission refers to the process by which a molecule releases energy, often in the form of light, as it transitions from a higher energy state to a lower energy state. This phenomenon is closely related to molecular interactions and electromagnetic radiation, playing a key role in understanding how molecules absorb and emit energy, which is fundamental in various scientific disciplines.
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. It plays a crucial role in molecular physics as it corresponds to specific energy transitions in molecules, allowing for the excitation of vibrational and rotational energy levels.
Infrared spectroscopy: Infrared spectroscopy is an analytical technique that utilizes the infrared region of the electromagnetic spectrum to identify and study chemical substances based on their molecular vibrations. This method is particularly useful for determining functional groups in organic compounds and understanding molecular structure, as it relates to energy levels associated with vibrational and rotational transitions within molecules.
Nanometer: A nanometer is a unit of measurement equal to one billionth of a meter (1 nm = 10^{-9} m). This tiny scale is crucial in understanding the dimensions of atoms and molecules, as well as the wavelengths of electromagnetic radiation. In this context, the nanometer helps bridge the gap between atomic and molecular scales and the larger scales involved in molecular energy levels, allowing for insights into how light interacts with matter at such small dimensions.
Perturbation theory: Perturbation theory is a mathematical approach used in quantum mechanics to find an approximate solution to a problem that cannot be solved exactly. It works by starting with a known exact solution of a simpler problem and then adding a small 'perturbation' or disturbance to account for the additional complexities of the more complicated system. This method is especially important in understanding how systems behave when subjected to external influences, like electromagnetic fields, which is relevant in analyzing molecular energy levels and selection rules.
Photoelectric effect: The photoelectric effect refers to the phenomenon where electrons are emitted from a material when it absorbs light or electromagnetic radiation. This effect demonstrates how energy from photons can be converted into kinetic energy of electrons, linking the behavior of light and matter in significant ways.
Planck's Constant: Planck's constant is a fundamental physical constant that describes the quantization of energy in quantum mechanics. It relates the energy of a photon to the frequency of its associated electromagnetic wave, establishing a crucial link between wave and particle behavior in molecular physics and spectroscopy.
Quantum state: A quantum state is a mathematical representation of a physical system in quantum mechanics, encapsulating all the information about the system's properties and behavior. It can be represented using wavefunctions, which describe the probabilities of finding a particle in various positions or states, and is essential for understanding how systems interact with each other and with external forces.
Quantum theory: Quantum theory is a fundamental framework in physics that describes the behavior of matter and energy at atomic and subatomic levels. It reveals that energy exists in discrete units called quanta, and that particles exhibit both wave-like and particle-like properties, leading to concepts like superposition and entanglement. This theory provides the basis for understanding phenomena such as absorption, emission, and scattering processes involving light and molecules, as well as how molecular energy levels relate to the electromagnetic spectrum.
Raman spectroscopy: Raman spectroscopy is an analytical technique used to observe vibrational, rotational, and other low-frequency modes in a system. This method provides unique information about molecular energy levels and chemical composition by measuring inelastic scattering of monochromatic light, typically from a laser. It connects to the electromagnetic spectrum by focusing on the interaction of light with molecular vibrations, which results in a shift in energy levels that corresponds to specific molecular structures.
Rotational energy levels: Rotational energy levels refer to the discrete energy states associated with the rotation of molecules, particularly diatomic and polyatomic molecules. These energy levels arise from the quantization of angular momentum, which dictates that molecules can only occupy specific rotational states. The transitions between these levels can be observed through interactions with electromagnetic radiation, linking them to the overall molecular energy landscape and how molecules absorb or emit light.
Speed of light: The speed of light is the constant speed at which electromagnetic waves propagate through a vacuum, measured to be approximately 299,792 kilometers per second (or about 186,282 miles per second). This fundamental constant plays a crucial role in understanding how light interacts with matter, particularly in relation to energy levels in molecules and the behavior of vibrational and rotational transitions in molecular physics.
Stark Effect: The Stark Effect refers to the phenomenon where the energy levels of atoms or molecules are shifted and split when subjected to an external electric field. This effect is significant in understanding molecular energy levels, as it influences how molecules interact with electromagnetic radiation, leading to observable spectral changes that can be analyzed for various applications in physics and chemistry.
Ultraviolet light: Ultraviolet light is a form of electromagnetic radiation with wavelengths shorter than visible light, typically ranging from about 10 nm to 400 nm. This type of light plays a critical role in various molecular processes, particularly in the excitation of electrons within molecules, which can lead to chemical reactions and changes in molecular energy levels.
Vibrational energy levels: Vibrational energy levels refer to the quantized states of vibrational motion that molecules can occupy, which are determined by the interactions of the atoms within the molecule. Each level corresponds to a specific amount of vibrational energy, and transitions between these levels occur when a molecule absorbs or emits energy, often in the form of infrared radiation. Understanding these levels is crucial for interpreting molecular spectra and analyzing molecular structures.
Wavefunction: A wavefunction is a mathematical function that describes the quantum state of a particle or system, encapsulating information about its position, momentum, and other physical properties. It plays a central role in quantum mechanics, particularly in predicting how systems evolve and interact, connecting to concepts like energy levels, transitions, and rules governing molecular behavior.
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