UV-Vis Spectrophotometry: Beer-Lambert Law and Calibration Curve
UV-Vis spectrophotometry: Beer-Lambert law and calibration curve
An educational simulator that connects the spectrum, wavelength, cuvette, absorbance, transmittance and calibration line used at the laboratory bench.
1. Select the system and wavelength
2. Beer-Lambert calculation
3. Educational spectrum and wavelength selection
The continuous line is an educational reconstruction centered on documented preset maxima. Click the plot to select a new wavelength.
4. Calibration curve
If measured absorbances are left blank, the tool generates the ideal Beer-Lambert series. Always use a semicolon ; to separate multiple values.
Equations used
For monochromatic radiation in a homogeneous solution, the commonly used Beer-Lambert expression is:
\[ A = \varepsilon\,b\,c \]
where A is absorbance, ε is the molar absorption coefficient, b is the optical path length and c is concentration.
Absorbance and transmittance are related by:
\[ A=-\log_{10}(T), \qquad T=\frac{I}{I_0}=10^{-A} \]
Choosing the analytical wavelength
Quantitative measurements are often made near an absorption maximum because sensitivity is higher. The best wavelength still depends on chemical species, solvent, pH and matrix, so every preset states the conditions to which its reference values apply.
The beam color in the diagram is an educational representation. In the visible region it approximately follows the selected wavelength; ultraviolet and near-infrared radiation are shown with conventional colors so that an invisible wavelength can still be represented on screen.
Why quartz cuvettes are used in the UV
The cuvette material must transmit in the spectral region used for the measurement. Common optical glass is mainly useful in the visible region, whereas high-performance fused silica can extend to about 200 nm. There is no single cutoff that applies to every cuvette: the actual range depends on material and product.
As educational reference values, Hellma lists 200–2500 nm for QS high-performance quartz, 260–2500 nm for UV quartz, 330–2500 nm for BF borosilicate glass and 360–2500 nm for OG optical glass. Some disposable UV plastic cuvettes are specified by the manufacturer for 230–900 nm, while PMMA examples are listed for 300–900 nm. The tool uses these ranges only to generate a warning; real work must follow the specification of the actual cuvette.
A standard optical path is often 10 mm = 1 cm, but path length is a measurement parameter and must not be assumed. It is editable in the tool and appears directly in the Beer-Lambert equation.
Good cuvette practice
- Do not touch the optical windows with your fingers.
- Remove droplets, residues and bubbles from the optical path.
- Insert the cuvette with the optical windows correctly aligned and keep orientation consistent for comparative measurements.
- Use a blank that matches the sample solvent, matrix and cuvette type.
- For quantitative work, always verify the manufacturer’s spectral range and optical path specification.
Calibration curve
Calibration mode can use actual measured absorbances or generate an ideal series. With measured data it performs an ordinary least-squares linear regression and reports slope, intercept and \(R^2\). The unknown concentration is calculated from the fitted line rather than directly from \(A=\varepsilon bc\).
When Beer-Lambert behavior may fail
Linearity can deteriorate because of high concentration, concentration-dependent chemical equilibria, association or dissociation, scattering, stray light, spectral bandwidth that is too wide relative to spectral structure, or blank and cuvette problems. The tool flags numerically extreme conditions but cannot replace an experimental linearity check for the instrument and analytical method.