Absorption Spectroscopy Simulator: Beer-Lambert Law & Line Profiles

simulator intermediate ~10 min
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A = 0.500 — 31.6% of light is transmitted

With ε = 5000 L/mol·cm, c = 0.1 mol/L, and l = 1 cm, the absorbance is 0.500, meaning 31.6% of incident light passes through the sample.

Formula

A = ε × c × l (Beer-Lambert law)
T = 10^(-A) = I / I₀ (transmittance)
α(λ) = A_peak × exp(-0.5 × ((λ - λ₀)/σ)²) (Gaussian line shape)

Shadows in the Spectrum

When white light passes through a gas or solution, atoms and molecules selectively absorb photons at specific wavelengths corresponding to their quantum energy levels. The transmitted light shows dark lines or bands where absorption occurred — the absorption spectrum. This technique, first exploited by Fraunhofer to map dark lines in sunlight, reveals the chemical identity and concentration of absorbing species.

Beer-Lambert: The Quantitative Foundation

August Beer and Johann Lambert independently established that light absorption increases linearly with concentration and path length. The combined law A = εcl connects measurable absorbance to molar absorptivity (a molecular property), concentration, and optical path. This elegant relationship makes spectrophotometry the workhorse of analytical chemistry — from clinical blood tests to environmental water monitoring.

Line Shape Physics

Real absorption lines are not infinitely sharp. Natural lifetime broadening (Lorentzian), thermal motion (Gaussian Doppler broadening), and collision effects (pressure broadening) each contribute to the observed line width. In solution, solvent cage effects and vibrational coupling produce broad bands rather than sharp lines. This simulation models Gaussian profiles and shows how line width affects peak height and integrated absorption.

Modern Absorption Spectroscopy

UV-Vis spectrophotometry remains the most common analytical technique in laboratories worldwide. Advances like cavity ring-down spectroscopy achieve effective path lengths of kilometers, detecting parts-per-trillion concentrations. Atmospheric remote sensing uses differential absorption to map pollutants from satellites. The fundamental principle is always the same: matter imprints its identity on light.

FAQ

What is the Beer-Lambert law?

The Beer-Lambert law states that absorbance is proportional to concentration and path length: A = εcl. It is the foundation of quantitative absorption spectroscopy, enabling concentration determination from measured light attenuation. The law holds for dilute, homogeneous solutions with monochromatic light.

What is absorbance vs transmittance?

Transmittance (T) is the fraction of light passing through a sample: T = I/I₀. Absorbance is the negative logarithm: A = -log₁₀(T). Absorbance is preferred because it is directly proportional to concentration (Beer-Lambert), making quantitative analysis straightforward.

What causes absorption lines?

Atoms and molecules absorb photons whose energy matches the difference between two quantum states. Electronic transitions produce UV-visible absorption; vibrational transitions produce infrared absorption; rotational transitions produce microwave absorption. Each transition produces a line at a characteristic wavelength.

When does Beer-Lambert law fail?

The law deviates at high concentrations (intermolecular interactions change ε), with polychromatic light (different wavelengths have different ε), when scattering occurs (turbid solutions), and when chemical equilibria shift with concentration. Practical absorbance measurements are most reliable between A = 0.1 and 2.0.

Sources

Embed

<iframe src="https://homo-deus.com/lab/spectroscopy/absorption-lines/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub