Atomic and Molecular Spectra Fundamentals

The electromagnetic spectrum is one continuous range of photon energies stretched across roughly twenty orders of magnitude, from gamma rays at femtometre wavelengths to radio waves at metres. Three relations tie wavelength, frequency and energy together. The speed of light c = λν fixes wavelength against frequency; Planck's relation E = hν fixes energy against frequency; and the wavenumber ν̃ = 1/λ (in cm⁻¹) is the form spectroscopists use because it scales linearly with energy and lands the working numbers between 100 and 4000 for vibrational work.

Forensic spectroscopy parks a technique at almost every region. Gamma rays drive Mössbauer spectroscopy and isotope counting; X-rays at 0.01 to 10 nm probe inner-shell electrons (XRF and XRD for paint, glass and gunshot residue); UV at 200 to 400 nm and visible light at 400 to 800 nm probe valence-electron transitions in conjugated organics and d-block metal complexes (UV-Vis quantitation of paracetamol, salicylate, methaemoglobin); near-IR and mid-IR at 4000 to 400 cm⁻¹ probe vibrational modes (FTIR-ATR identification of unknown powders, paint chips, explosive residues); microwave drives rotational spectroscopy in the gas phase; radio frequencies at MHz drive nuclear spin transitions in NMR for structural elucidation of seized drugs.

The reason each region drives a different technique is straightforward: the photon energy must match the spacing of the transition you want to excite. Electronic transitions in organic molecules sit at a few electron-volts and that is the UV-Vis region. Vibrational transitions sit at tenths of an electron-volt and that is the IR region. Rotational transitions sit at thousandths of an electron-volt and that is the microwave region. Nuclear spin transitions in a magnetic field sit at micro-electron-volts and that is the radio region. Using the wrong spectral region for the target transition produces no signal: photon energy must match level spacing for the interaction to occur.

An isolated atom in the gas phase has a set of allowed electronic states, each with a defined energy. The Bohr model fixes hydrogen's levels at Eₙ = -13.6 / n² eV, and the same logic extends to multi-electron atoms with corrections for shielding and spin-orbit coupling. When an atom absorbs a photon at exactly the energy difference between two states, an electron jumps to the upper state. When the excited atom relaxes, it releases the same energy as a photon. Because the levels are sharp and the transitions are discrete, the resulting spectrum is a pattern of sharp lines, each line at a wavelength characteristic of the element.

Sodium gives the famous 589 nm doublet (the D-lines) from the 3p to 3s transition. Mercury gives 254 nm in the deep UV from a 6p to 6s drop, which is why low-pressure Hg lamps are the workhorse source for UV sterilisation and atomic absorption. Calcium gives 422.7 nm; potassium gives 766.5 nm; lead gives 283.3 nm; arsenic gives 193.7 nm. Every element on the periodic table has a unique line-pattern fingerprint, and a flame, plasma or X-ray excitation source plus a wavelength-resolved detector is enough to tell one from another.

This is the entire physical basis of atomic spectroscopy in a forensic lab. AAS reads the absorbance of a hollow-cathode lamp's element-specific line by atomic vapour from the sample (lead in a paint chip dissolved in nitric acid; mercury in fish tissue cold-vapour generated). AES, ICP-OES and ICP-MS excite the sample in a flame or argon plasma and read the emission lines. XRF excites inner-shell electrons with X-rays and reads the characteristic fluorescence lines. The instrument architecture differs; the physics is one rule: each element radiates and absorbs at its own set of wavelengths.

A practical caution. Real flame and plasma sources broaden lines through Doppler and pressure broadening, so what looks sharp in a textbook is a few picometres wide on a real spectrometer. Spectral interference (overlapping lines from different elements) is the recurring nuisance, especially in matrix-rich samples. The Indian Standards Bureau (BIS) IS 12702 series and the CFSL toxicology SOPs for AAS prescribe interference-correction protocols (Zeeman background correction, deuterium-lamp correction, matrix-matched calibration) for exactly this reason.

A molecule has all the electronic levels an atom has, but it also vibrates and rotates. Each electronic state therefore carries a stack of vibrational sub-levels, and each vibrational sub-level carries a stack of rotational sub-levels. When a photon promotes the molecule from a ground vibrational level of the ground electronic state to some vibrational level of the excited electronic state, many transitions of slightly different energy are possible. The result is not a single sharp line but an envelope of closely spaced lines that the spectrometer reads as a band.

The vibrational modes of a non-linear molecule with N atoms are 3N - 6 in number (3N - 5 for linear molecules). They split into two families. Stretching modes change bond lengths, either symmetrically (both bonds extending and contracting in phase) or asymmetrically (one extending while the other contracts). Bending modes change bond angles, with four named varieties: scissoring (in-plane symmetric bend), rocking (in-plane asymmetric bend), wagging (out-of-plane symmetric bend) and twisting (out-of-plane asymmetric bend). Each mode absorbs at a characteristic IR frequency that depends on the masses and the bond force constant. A C=O stretch sits near 1715 cm⁻¹; a broad O-H stretch sits between 3200 and 3600 cm⁻¹; an aromatic C-H stretch sits between 3000 and 3100 cm⁻¹. These are the diagnostic group frequencies that anchor IR identification.

The IR-Raman complementarity rule follows directly from symmetry. For a centrosymmetric molecule (one with a centre of inversion, like CO₂ or benzene), a vibrational mode is either IR-active or Raman-active, never both. Symmetric stretches change polarisability without changing dipole moment and so are Raman-active and IR-silent; asymmetric stretches change dipole moment and so are IR-active and Raman-silent. The two techniques therefore see complementary parts of the same vibrational manifold, which is why a complete vibrational characterisation of an unknown solid in forensic practice often runs both an FTIR-ATR scan and a Raman scan on the same sample.

Rotational fine structure becomes visible only in low-pressure gas-phase IR (a forensic lab almost never sees it because samples are condensed phases). NMR's spin transitions live in the radio region and probe nuclear, not electronic, energy levels in an applied magnetic field. ESR (also called EPR) does the same thing for unpaired electrons in radicals and transition-metal complexes. Both techniques are part of the same physical idea: a quantised level spacing, a photon of matched energy, a measurable transition.

When a photon meets a molecule, three things can happen. The photon can be absorbed, promoting the molecule to an excited state and disappearing from the beam. The molecule can return to the ground state and emit a photon, often at a different wavelength because some of the excitation energy has dissipated as heat. Or the photon can scatter off the molecule, either elastically (no energy change) or inelastically (a small energy exchange with a vibrational mode). Each outcome is the basis of a family of techniques.

Absorption techniques include UV-Vis (electronic transitions in solution), IR and FTIR (vibrational transitions), AAS (electronic transitions in atomic vapour) and NMR (nuclear-spin transitions in a magnetic field). The Beer-Lambert law A = εbc applies wherever absorption is read against a baseline: absorbance is linearly proportional to analyte concentration over a working range, with ε the molar absorptivity, b the path length and c the concentration. Quantitation under Beer-Lambert is the bread-and-butter use of every absorption spectrometer in the lab.

Emission techniques include atomic emission (AES, ICP-OES) where excited atoms in a flame or plasma radiate their characteristic lines, and molecular fluorescence and phosphorescence where electronically excited molecules drop back to the ground state. Fluorescence is fast (nanoseconds) because the singlet-to-singlet drop is spin-allowed. Phosphorescence is slow (milliseconds to seconds) because it goes through an intermediate triplet state and the triplet-to-singlet drop is spin-forbidden by selection rules. The slow time-scale is exploited in phosphorescence imaging and in time-resolved measurements that suppress prompt fluorescence background.

Scattering techniques include Rayleigh scattering (elastic, no energy change, dominates atmospheric optics and is the reason the sky is blue) and Raman scattering (inelastic, the photon loses or gains energy equal to a vibrational quantum). Raman scattering has direct forensic applications: a molecule shifts the scattered light by its vibrational frequencies, producing a fingerprint complementary to IR. Modern handheld Raman units used by NSG and CISF for explosive screening at airports are running this physics in a 1.5 kg case.

The mapping is mechanical once the physics is internalised. UV-Vis at 200 to 800 nm probes π-electron transitions in conjugated organics and d-electron transitions in transition-metal complexes; that is why a methaemoglobin band sits at 630 nm and a paracetamol-phenolate band sits at 245 nm. IR at 4000 to 400 cm⁻¹ probes vibrational modes; that is why the carbonyl of an unknown ester sits at 1735 cm⁻¹ and the broad O-H of an alcohol sits at 3300 cm⁻¹. NMR in the radio region (60 to 900 MHz on commercial superconducting magnets) probes nuclear spin transitions; that is why ¹H sits near 4.7 ppm for water and 7.3 ppm for benzene, and that is why a 600 MHz NMR can resolve diastereotopic protons in a seized methamphetamine batch that GC-MS cannot.

X-ray techniques probe inner-shell electrons. XRF excites a K-shell or L-shell electron, and the vacancy is filled by an outer-shell drop that emits a characteristic X-ray photon (the Pb-Lα line at 10.55 keV, the Sb-Kα line at 26.36 keV, the Ba-Lα line at 4.47 keV). These three lines are the SEM-EDS fingerprint for gunshot residue particles in Indian forensic-physics labs. XRD reads Bragg reflections from crystalline planes, which identifies the polymorph of a drug, the cement composition of a concrete chip, or the mineral phase of a soil sample.

The forensic relevance of the line-vs-band distinction is direct. Line spectra fingerprint elements; that is why AAS and ICP-OES are the techniques of choice for "is there arsenic in this viscera, and how much". Band spectra fingerprint molecules; that is why FTIR-ATR is the technique of choice for "is this seized white powder methamphetamine, sucrose or talc". Isotope shifts (a small wavelength shift between isotopologues) carry origin information; isotope-ratio mass spectrometry of the strontium-87 to strontium-86 ratio in tooth enamel localises the geography of an unidentified body, a technique that the Centre for Cellular and Molecular Biology (CCMB) Hyderabad and a handful of CSIR labs run for cold-case anthropology work.

The Indian institutional context is worth naming once. The Bureau of Indian Standards publishes the IS 12702 (atomic absorption), IS 11888 (atomic emission), and IS 7016 (UV-Vis methods) series that codify how a forensic lab calibrates and runs each technique. The CFSL training pipeline at CFSL Chandigarh teaches this physics first, before any student touches an instrument; the IIT Bombay SAIF, IIT Madras SAIF and IISc Bangalore central facilities maintain the high-end instruments that state SFSLs send referral samples to. Knowing the physics is what lets a working examiner read a spectrum in a referral report and decide whether the conclusion is sound or has confused a Raman shift for an IR band.