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.

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.

Electromagnetic Spectrum and Molecular Energy

Electromagnetic Radiation Characteristics

• The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation, from low-frequency radio waves to high-frequency gamma rays
• Electromagnetic radiation can be described as a wave with a specific wavelength, frequency, and energy, related by the equation $E = hν$, where $E$ is energy, $h$ is Planck's constant, and $ν$ is frequency
• The energy of a photon determines the region of the electromagnetic spectrum involved in a molecular transition (microwave, infrared, visible, or ultraviolet)

Molecular Energy Levels and Transitions

• Molecules have discrete, quantized energy levels that correspond to different electronic, vibrational, and rotational states
• 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
  1. Absorption: molecule absorbs a photon and transitions to a higher energy level
  2. Emission: molecule emits a photon and transitions to a lower energy level

Regions of the Electromagnetic Spectrum

Low Energy Regions

• The microwave region corresponds to transitions between rotational energy levels in molecules
  • Wavelengths between 1 mm and 1 m
  • Example: microwave spectroscopy used to study molecular rotations
• The infrared region corresponds to transitions between vibrational energy levels in molecules
  • Wavelengths between 700 nm and 1 mm
  • Example: IR spectroscopy used to identify functional groups in organic molecules

High Energy Regions

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

Quantized Energy Levels in Molecules

Origin and Characterization of Quantized Energy Levels

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

Spectroscopic Applications

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

Photon Energy vs Frequency and Wavelength

Energy-Frequency Relationship

• The energy of a photon is directly proportional to its frequency, as described by the equation $E = hν$, where $E$ is energy, $h$ is Planck's constant, and $ν$ is frequency
• Higher frequency photons have higher energies, while lower frequency photons have lower energies
• The relationship between photon energy and frequency is linear, with the slope determined by Planck's constant
  • 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

Energy-Wavelength Relationship

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