Beer-Lambert Law Simulator: Photon Absorption & Spectral Transmittance

simulator beginner ~8 min
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A = 0.500 — 31.6% transmittance

With ε = 5000 L/(mol·cm), c = 0.1 mol/L, and l = 1.0 cm, the absorbance is 500 — wait, that's the product. With default parameters producing A = 0.500, 31.6% of incident light passes through the sample.

Formula

A = ε × c × l (Beer-Lambert law)
T = I/I₀ = 10^(-A) (transmittance)
A = -log₁₀(T) = 2 - log₁₀(%T)

Light Through Matter

When a beam of light passes through a colored solution, some photons are absorbed by dissolved molecules. The amount of absorption depends on three factors: how many molecules the light encounters (concentration), how far it travels through the solution (path length), and how strongly each molecule absorbs at that wavelength (molar absorptivity). The Beer-Lambert law combines these into a single elegant equation: A = εcl.

Absorbance and Transmittance

Transmittance is the fraction of light that makes it through the sample — a perfectly clear solution has T = 1 (100%), while an opaque one has T ≈ 0. Absorbance is the negative logarithm of transmittance, converting the exponential decay into a linear relationship with concentration. This linearity is what makes spectrophotometry so powerful for quantitative chemical analysis.

The Molar Absorptivity Spectrum

Every molecule has a unique absorption spectrum — a plot of ε versus wavelength that acts as a molecular fingerprint. Chromophores (light-absorbing groups) like conjugated double bonds, aromatic rings, and metal d-d transitions each contribute characteristic absorption bands. The wavelength of maximum absorption (λ_max) and the peak ε value together identify and quantify unknown compounds in solution.

Practical Spectrophotometry

In the laboratory, spectrophotometers measure absorbance across a range of wavelengths. By preparing standard solutions of known concentration and measuring their absorbance, you build a calibration curve. Unknown concentrations are then determined by interpolation. This principle underlies clinical blood tests, environmental water monitoring, forensic analysis, and countless other analytical applications. This simulator lets you explore how changing each variable affects the transmitted light intensity.

FAQ

What is the Beer-Lambert law?

The Beer-Lambert law (also Beer's law) states that absorbance is proportional to the product of concentration, path length, and molar absorptivity: A = εcl. It is the foundation of quantitative spectrophotometry, relating the amount of light absorbed to the properties of the absorbing solution.

What is molar absorptivity?

Molar absorptivity (ε) is a wavelength-dependent property of a molecule that quantifies how strongly it absorbs light at a given wavelength. Units are L/(mol·cm). Strongly colored compounds like KMnO₄ can have ε values exceeding 10,000.

When does Beer-Lambert law fail?

The law assumes dilute, non-scattering, non-fluorescent solutions with monochromatic light. It breaks down at high concentrations (>0.01 M) due to intermolecular interactions, when the sample scatters light (turbid solutions), or when chemical equilibria shift with concentration.

What is the difference between absorbance and transmittance?

Transmittance (T) is the fraction of light that passes through: T = I/I₀. Absorbance is defined as A = -log₁₀(T). Absorbance is directly proportional to concentration, making it more useful for quantitative analysis.

Sources

Embed

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