Spectroscopy
A spectrum connects a physical interaction to a measured signal. Before assigning a peak, identify the axes and the mechanism that creates the signal.
Physical origin of the signal
For a photon, E = hν = hc/λ. If matter changes between two states separated by an energy ΔE, the resonant photon frequency satisfies ΔE = hν. A larger energy separation therefore corresponds to a higher frequency and a shorter wavelength.
This does not mean that every possible energy difference produces a strong line. Quantum-mechanical selection rules and the detailed coupling between radiation and matter determine whether a transition is allowed and how intense it is.
In absorption spectroscopy, incident radiation loses particular photon energies because the sample is promoted to higher-energy states. In emission spectroscopy, an excited sample releases photons as it moves to lower-energy states. The same energy gap can therefore appear as an absorption feature in one experiment and an emission feature in another.
In scattering spectroscopy, the detected photon has interacted with the sample and changed direction. Most scattering is elastic, but in Raman spectroscopy a small fraction of photons exchange energy with molecular vibrations. The frequency shift of the scattered light then reveals vibrational information without measuring ordinary IR absorption.
An isolated atom has electronic energy levels. A transition between two of them produces a well-defined photon energy, so atomic spectra often contain relatively narrow lines. Hydrogen is the classic example: the visible Balmer lines correspond to transitions ending at n = 2, while the Lyman and Paschen series lie mainly in the ultraviolet and infrared.
Molecules have more ways to store energy. Electronic states contain vibrational sublevels, and those contain rotational structure. Many closely spaced transitions can therefore overlap into bands. Condensed phases broaden them further through collisions and interactions with neighbouring molecules. A molecular spectrum is not “messier because the instrument is worse”; much of that complexity belongs to the molecule itself.
Reading a spectrum
The horizontal axis is not universal. Depending on the technique it may be wavelength λ, frequency ν, photon energy E, wavenumber ṽ in cm⁻¹, or NMR chemical shift δ in ppm. The vertical axis might be intensity, absorbance, transmittance, emission counts or another detector response.
This matters because the visual direction can reverse. In IR spectroscopy, spectra are often plotted with high wavenumber on the left. A transmittance spectrum shows absorption as downward features; an absorbance spectrum shows the same absorptions upward. Before assigning chemistry to a peak, identify the axes, units and plotting convention.
| Technique | Interaction | Typical information |
|---|---|---|
| UV–visible | Electronic transitions | Absorption, colour, concentration |
| IR | Vibrations | Bonds and functional groups |
| Raman | Inelastic scattering | Vibrations complementary to IR |
| NMR | Nuclear spins | Local environments and connectivity |
Common techniques
UV–visible
UV–visible radiation commonly promotes valence electrons between molecular orbitals or electronic states. Conjugated π systems and transition-metal complexes are frequent examples because their energy separations fall in the UV or visible range. Absorption of visible wavelengths also explains colour: a solution appears coloured because some parts of visible light are removed more strongly than others.
UV–Vis is especially useful when the aim is not only to identify an absorbing species but to measure its concentration. The central relation is the Beer–Lambert law:
A = εbc
Here A is absorbance (dimensionless), ε is the molar absorptivity, often in L mol⁻¹ cm⁻¹, b is optical path length in cm and c is concentration in mol L⁻¹. At a chosen wavelength, absorbance is proportional to concentration when the chemical form is stable and the experimental conditions stay in the linear regime.
Infrared
Infrared radiation can drive transitions between molecular vibrational states. Stretching and bending frequencies depend on bond stiffness, the masses of the atoms and the molecular environment. A strong C=O stretching band, for example, appears at a very different wavenumber from an O–H stretching region.
A vibration absorbs IR only if it produces a change in the molecule’s dipole moment. This selection requirement is why symmetry matters and why IR and Raman spectra often complement each other. The crowded lower-wavenumber fingerprint region can be highly characteristic of a molecule even when individual bands are difficult to assign one by one.
Raman
Raman spectroscopy measures the small inelastic component of scattered light. A molecular vibration is Raman-active when it changes the molecule’s polarizability. IR activity instead depends on a change in dipole moment. Because those conditions differ, a vibration that is weak or absent in IR may be strong in Raman, especially in symmetric molecules.
This complementarity is more useful than declaring one technique “better”. The experiment should be chosen according to the physical interaction that can reveal the feature of interest.
NMR
Nuclear magnetic resonance does not primarily probe molecular vibrations or electronic colour. Certain nuclei possess spin and, in a magnetic field, can occupy different magnetic energy states. Radiofrequency radiation drives transitions between them.
The local electron distribution slightly shields a nucleus from the applied field. That is why chemically different hydrogens or carbons resonate at different chemical shifts, usually reported in ppm. Signal number, chemical shift, integrated area and spin–spin splitting carry different structural information. NMR is therefore powerful for reconstructing how atoms are connected, not merely for asking which functional group is present.
Calculations
Beer–Lambert
An analyte has ε = 1.50 × 10⁴ L mol⁻¹ cm⁻¹ at its absorption maximum. A 1.00 cm cuvette gives A = 0.720. Then:
c = A/(εb) = 0.720 / [(1.50 × 10⁴)(1.00)] = 4.80 × 10⁻⁵ mol L⁻¹.
The calculation is simple; the experimental judgement is not. A non-zero blank, stray light, scattering, a chemical equilibrium that changes with concentration, or absorbance values outside the useful linear range can all make the apparent straight-line relation unreliable. Good spectrophotometry therefore uses blanks and usually a calibration series rather than trusting one equation blindly.
Photon energy
A line at 486.1 nm corresponds to a photon energy of approximately:
E ≈ 1240 eV·nm / 486.1 nm = 2.55 eV.
If that line is produced by an atomic transition, 2.55 eV is the energy difference between the two participating states. The wavelength is not an arbitrary colour label; it is an energy measurement.
Real spectra and instrumentation
Atoms of each element have a characteristic pattern of allowed energy differences. Excited sodium, hydrogen, helium or iron therefore emit and absorb different sets of wavelengths. Laboratory atomic spectroscopy uses those signatures for elemental analysis; astronomy uses the same physics to infer the composition of stellar atmospheres without collecting a physical sample.
A line position identifies an energy difference. A line intensity depends on additional factors such as the population of the states, transition probability, amount of species present and instrument response. Intensity is therefore not a direct measure of “how much energy that level contains”.
No real spectral line is infinitely narrow. A finite excited-state lifetime produces natural broadening. Thermal motion causes Doppler broadening because moving emitters or absorbers see slightly shifted frequencies. Collisions cause pressure broadening. The instrument itself adds a finite response width.
Resolution describes the ability to distinguish nearby spectral features. Increasing resolution can separate peaks that previously merged, but it does not create information that the physical sample never encoded. Instrument settings also trade resolution against signal strength, acquisition time and noise.
Different instruments look different, but most perform the same logical steps: generate or accept radiation, select or encode its spectral content, make it interact with the sample, detect the response and convert that response into a spectrum. A dispersive UV–Vis instrument may use a grating or monochromator to select wavelengths sequentially. Fourier-transform IR spectroscopy instead records an interferogram containing many frequencies at once and mathematically transforms it into a spectrum.
The displayed trace is therefore already the result of optics, electronics and data processing. Background subtraction, detector sensitivity, calibration and baseline correction are part of the measurement—not cosmetic steps added after the “real” science.
Analytical interpretation
Mass spectrometry is routinely taught beside IR, UV–Vis and NMR because all are central to chemical identification. Strictly, however, mass spectrometry does not detect electromagnetic absorption or emission as a function of photon energy. It ionises species and separates or analyses ions according to their mass-to-charge ratio m/z.
The distinction matters because the information is complementary. Mass spectrometry can constrain molecular mass and formula or reveal fragmentation; IR can identify bond types; NMR can reveal local atomic environments and connectivity; UV–Vis can probe electronic structure and concentration. Modern structure determination becomes far stronger when those independent clues agree.
- Identify the technique. IR, UV–Vis, NMR and atomic emission do not use the same axes or interpretive rules.
- Read axes and units. Never assign a peak before doing this.
- Separate position, intensity and width. They answer different questions.
- Look for patterns, not isolated peaks. Series, band shapes, splitting and relative intensities are often more informative than one feature.
- Check physical plausibility. Does the proposed transition or functional group fit the rest of the sample chemistry?
- Combine techniques. Treat independent spectra as constraints on one structure rather than as separate identification games.
A peak assignment is a hypothesis supported by physical models and comparison, not a magic label attached by the instrument. Overlapping bands, mixtures, solvent signals, fluorescence, scattering, saturation, matrix effects and imperfect calibration can all mislead interpretation. Database matching is powerful, but a numerical match without chemical context can still be wrong.
The strongest conclusion is usually the one supported by several independent observations: the right peak positions, sensible intensities, appropriate line shapes and agreement with another analytical method.
Exercises
Beer–Lambert
Two solutions of the same species are measured under identical conditions. The second concentration is doubled and the linear regime holds. What happens to absorbance?
Solution
It doubles because A = εbc and ε and b are unchanged.
Choosing a technique
You need to distinguish several proton environments in an organic molecule. Which technique is most direct?
Solution
NMR, because chemical shift depends on the local electronic environment of the observed nuclei.