Spectroscopy and Molecular Absorption (4D) - MCAT Chemical and Physical Foundations of Biological Systems

Radiofrequency (MHz range). Radiofrequency matches the energy differences between nuclear spin states in a magnetic field for proton NMR.

About $1500\text{ cm}^{-1}$ to $500\text{ cm}^{-1}$. This range contains complex, molecule-specific bands useful for identifying unique molecular structures.

About $1700\text{ cm}^{-1}$ (roughly $1650$–$1750\text{ cm}^{-1}$). Carbonyl stretches absorb in this range due to the bond's strength and reduced mass in the harmonic oscillator model.

$\pi \rightarrow \pi^$ (and $n \rightarrow \pi^$). These low-energy electronic promotions occur in conjugated systems, absorbing in the UV-Vis region.

UV and visible light (about $200\text{ nm}$ to $800\text{ nm}$). UV-Vis light provides energy for electronic transitions in molecules, leading to absorption spectra in that range.

Bond vibrations (stretching and bending). IR radiation energies align with vibrational transitions, causing bonds to stretch or bend upon absorption.

Vibration must change the dipole moment. For IR absorption, the vibration must alter the molecule's dipole to interact with the electric field.

$A = \varepsilon \ell c$. Absorbance is proportional to molar absorptivity, path length, and concentration in dilute solutions.

Mid-IR, about $4000\text{ cm}^{-1}$ to $400\text{ cm}^{-1}$. Mid-IR radiation matches the energy of molecular vibrations, enabling absorption in IR spectroscopy.

$\tilde{\nu} = \frac{1}{\lambda}$. Wavenumber is the reciprocal of wavelength, often used in spectroscopy for its proportionality to energy.

$A = \log_{10}!\left(\frac{I_0}{I}\right)$. Absorbance quantifies light absorption as the logarithm of the ratio of incident to transmitted intensity.

$T = \frac{I}{I_0}$. Transmittance measures the fraction of incident light that passes through the sample without absorption.

$A = -\log_{10}(T)$. Absorbance is the negative logarithm of transmittance, linking the two in spectroscopic measurements.

Absorbance doubles. Per Beer-Lambert law, absorbance is directly proportional to concentration when other factors are constant.

$A$ doubles. Absorbance scales linearly with path length according to the Beer-Lambert law, assuming constant concentration and absorptivity.

Molar absorptivity, $\varepsilon$. Molar absorptivity is the constant of proportionality in Beer-Lambert law, derived by rearranging the equation.

$\text{L},\text{mol}^{-1},\text{cm}^{-1}$. These units arise from absorbance (unitless), path length in cm, and concentration in mol/L.

Wavelength of maximum absorbance. It indicates the wavelength where the molecule absorbs most strongly, corresponding to peak electronic transition efficiency.

Increased conjugation (smaller $\Delta E$). Extended conjugation reduces the HOMO-LUMO energy gap, shifting absorption to longer wavelengths.

Hypsochromic (blue) shift. Shorter wavelength absorption implies higher energy transitions, termed hypsochromic or blue shift.

$\omega_0 = \gamma B_0$. Resonance occurs when the applied frequency matches the Larmor (angular) frequency, given by gyromagnetic ratio times magnetic field.

$E = h\nu$. Photon energy is directly proportional to its frequency, as described by Planck's relation with constant $h$.

$E = \frac{hc}{\lambda}$. Photon energy is inversely proportional to wavelength, derived from combining Planck's relation and the speed of light.

Wavenumber, $\text{cm}^{-1}$. IR spectra use wavenumber for its direct proportionality to vibrational energy and frequency.