Molecular Spectroscopy: Reading a Fingerprint Made of Light

Why molecules absorb only certain frequencies

A molecule is not a rigid object — its bonds stretch, bend and twist like tiny springs connecting the nuclei, and quantum mechanics restricts those motions to a discrete ladder of vibrational energy levels, not a continuous range. A photon is absorbed only if its energy E = hν matches the gap between two of those levels exactly; any other frequency passes straight through. Because the allowed energy gaps are fixed by the masses of the atoms and the stiffness of the bond holding them together, every distinct bond and functional group produces its own characteristic set of absorption frequencies — which is why an infrared spectrum acts as a fingerprint you can use to identify a molecule.

E_photon = h * nu                         // Planck relation
nu_vib ~= (1 / 2*pi) * sqrt(k_bond / mu)   // simple harmonic-oscillator estimate
mu = (m1 * m2) / (m1 + m2)                 // reduced mass of the two bonded atoms

The simple harmonic-oscillator model already explains a lot: a stiffer bond (larger force constant k) or lighter atoms (smaller reduced mass μ) both push the vibrational frequency higher. This is why the light C–H stretch absorbs around 2900–3100 cm⁻¹ while the heavier, similarly-stiff C–Cl stretch absorbs at a much lower 600–800 cm⁻¹ — the mass in the denominator dominates.

Why bands are bands, not lines

A single, isolated, motionless molecule at absolute zero would show sharp spectral lines. Real samples don't, for three compounding reasons. First, Doppler broadening: molecules are in constant thermal motion, and the random spread of velocities toward and away from the light source smears each transition frequency by the Doppler effect, an effect that grows with the square root of temperature. Second, collisional (pressure) broadening: collisions between molecules interrupt the vibration mid-cycle and shorten its effective lifetime, and a shorter-lived state has a less sharply defined energy by the quantum uncertainty principle — more frequent collisions at higher pressure or concentration broaden the line further. Third, each vibrational transition is accompanied by many simultaneous, closely spaced rotational transitions (rotational fine structure), which is what turns a single vibrational absorption into a broad band with internal structure rather than one infinitely sharp spike.

Beer–Lambert: how much light a sample removes

Once you know a sample absorbs at a given frequency, the Beer–Lambert law tells you how much of the light is actually removed as it passes through: absorbance grows linearly with both the concentration of absorbing molecules and the path length the light travels through the sample.

A = epsilon * c * l                 // Beer-Lambert law
I = I0 * 10^(-A) = I0 * 10^(-epsilon*c*l)   // transmitted intensity
epsilon = molar absorptivity (per band, per molecule)

Doubling the concentration or doubling the path length both double the absorbance A, but because transmitted intensity depends on 10 raised to the power of −A, the transmitted light drops exponentially, not linearly, as either quantity increases. This is the working principle behind every laboratory UV-Vis and IR spectrophotometer, and behind atmospheric remote sensing of gases like CO2 and methane, which are identified and quantified by exactly this absorption-versus-concentration relationship.

Reading a real spectrum

Put the three ideas together and a spectrum tells a full story: where a band sits (frequency) identifies which bond or functional group is vibrating; how wide it is reports the temperature and pressure of the sample through Doppler and collisional broadening; and how deep it is, via Beer–Lambert, reports how much of the absorbing molecule is present. This is exactly what the simulation on this page lets you explore directly — turning temperature up visibly broadens the bands, raising concentration visibly deepens them, and each is a separate, independently tunable knob on the same underlying physics.

Frequently asked questions

Try it live

Everything above runs in your browser — open Molecular Spectroscopy and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.