12.5 Spectroscopy and the Electromagnetic Spectrum

Electromagnetic radiation interacts with molecules in fascinating ways. Light waves can cause molecules to vibrate, rotate, or undergo electronic transitions. These interactions form the basis of spectroscopy, a powerful tool for analyzing molecular structures.

Different types of radiation excite different molecular motions. Infrared light causes bond vibrations, while UV and visible light trigger electronic transitions. By studying how molecules absorb and emit radiation, we can deduce their structures and properties.

Electromagnetic Radiation and Spectroscopy

Electromagnetic radiation and organic molecules

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Electromagnetic radiation consists of oscillating electric and magnetic fields that travel through space as waves characterized by wavelength ($\lambda$), frequency ($\nu$), and energy ($E$)

Molecules can absorb electromagnetic radiation when the energy of the photon matches the energy difference between two molecular energy levels causes molecules to transition from a lower energy state to a higher energy state

Different types of molecular motions and transitions require different amounts of energy

• Stretching and bending vibrations of bonds absorb infrared (IR) radiation (molecular vibrations)
• Electronic transitions absorb ultraviolet (UV) and visible light (colors) Molecules absorb radiation at specific wavelengths corresponding to the energy required for a particular transition while wavelengths not absorbed by the molecule are transmitted through the sample (transparent materials)

Energy levels and transitions

Molecules have discrete energy levels corresponding to different states:

• Ground state: lowest energy level
• Excited states: higher energy levels Transitions between energy levels can occur through:
• Absorption: molecule gains energy by absorbing a photon
• Emission: molecule loses energy by emitting a photon Electronic transitions involve changes in the distribution of electrons in molecular orbitals, typically requiring higher energies than molecular vibrations

Photon energy calculations

The Planck equation relates the energy of a photon to its frequency and wavelength: $E = h\nu = \frac{hc}{\lambda}$

• $E$ is the energy of the photon (in joules)
• $h$ is Planck's constant ($6.626 \times 10^{-34}$ J⋅s)
• $\nu$ is the frequency of the electromagnetic wave (in Hz)
• $c$ is the speed of light ($2.998 \times 10^8$ m/s)
• $\lambda$ is the wavelength of the electromagnetic wave (in meters) Frequency and wavelength are inversely proportional
• Higher frequency corresponds to shorter wavelength and higher energy (gamma rays)
• Lower frequency corresponds to longer wavelength and lower energy (radio waves) Different regions of the electromagnetic spectrum have different wavelengths and energies:

1. Radio waves: longest wavelengths, lowest energies
2. Microwaves (ovens)
3. Infrared (IR) (heat lamps)
4. Visible light
5. Ultraviolet (UV) (black lights)
6. X-rays (medical imaging)
7. Gamma rays: shortest wavelengths, highest energies (nuclear radiation)

Interpretation of infrared spectra

Infrared (IR) spectroscopy measures the absorption of IR radiation by a sample typically presented as a plot of percent transmittance (%T) vs. wavenumber ($\tilde{\nu}$) or wavelength ($\lambda$)

• Wavenumber is the reciprocal of wavelength, expressed in cm$^{-1}$ Different functional groups absorb IR radiation at characteristic wavelengths
• O-H and N-H stretching vibrations: 3200-3600 cm$^{-1}$ (alcohols, amines)
• C-H stretching vibrations: 2800-3300 cm$^{-1}$ (alkanes)
• C=O stretching vibrations: 1600-1800 cm$^{-1}$ (ketones, aldehydes)
• C=C stretching vibrations: 1600-1700 cm$^{-1}$ (alkenes) %T represents the amount of IR radiation transmitted through the sample
• Lower %T indicates greater absorption at a particular wavelength
• Absorption peaks appear as downward-pointing peaks or dips in the spectrum Presence of absorption peaks at characteristic wavelengths indicates the presence of specific functional groups while absence of expected absorption peaks suggests the absence of certain functional groups

Comparing the IR spectrum of an unknown compound to reference spectra can aid in structural elucidation (identifying unknown compounds)

The Beer-Lambert law relates the absorption of light to the properties of the sample through which the light is traveling, allowing for quantitative analysis of solution concentrations