Spectrophotometer and Beer-Lambert Law Simulator
Equations in this simulation
| A | absorbance | no units; each unit of A cuts the light ten times | |
|---|---|---|---|
| T | transmittance | the share of the light that gets through the sample, compared with a blank of the solvent alone |
With the current values:
| ε | absorptivity at this wavelength | in M⁻¹ cm⁻¹ for the salts; for the protein and DNA, per mg/mL or per µg/mL per cm | |
|---|---|---|---|
| l | Path length l | the distance the light travels through the solution | |
| c | concentration | from Concentration (% of the range; the value is in the results) |
With the current values:
| m, b | slope and intercept of the standard curve | fitted by least squares to the standards you add; R² says how straight they are |
|---|
With the current values:
| s | stray light | light of other wavelengths that reaches the detector anyway; it caps the absorbance an instrument can read near −log₁₀ s = 3 |
|---|
With the current values:
How to use the spectrophotometer simulator
- Pick a solution, a wavelength and a concentration. Light from the lamp is split into colors by the monochromator, one narrow band passes the slit, goes through the cuvette and reaches the detector, which reads the absorbance compared with a blank of the solvent alone. Press Go to the peak to jump to the wavelength the solution absorbs most.
- Watch the absorbance rise in proportion to concentration and path length, as the Beer-Lambert law says, and the solution's color deepen. The chart shows the whole absorption spectrum: the measured curve next to Beer-Lambert alone. Push the concentration until the absorbance passes 2 or 3 and the measured curve flattens because of stray light; widen the slit on the narrow permanganate peaks, or choose a plastic cuvette in the ultraviolet, to see other ways readings go wrong.
- Build a standard curve: set several concentrations, pressing Add this reading to the standard curve each time, then Measure the unknown. The fitted line gives the unknown's concentration, and the results also show what it actually was. The Beer-Lambert Law Calculator and the Standard Curve Calculator do the same with your own readings.
Frequently asked questions
What is the Beer-Lambert law?
A = ε l c: absorbance equals the absorptivity of the substance at that wavelength, times the path length of the light through the solution, times the concentration. Because absorbance is logarithmic, A = 1 means 10% of the light gets through and A = 2 means 1%. The law is what lets a spectrophotometer measure concentration.
Why measure at the peak wavelength?
At λmax the absorbance is largest, so the measurement is most sensitive, and the curve is flat there, so a small error in the wavelength or a wide slit changes the reading least. DNA is measured at 260 nm and protein at 280 nm for this reason.
Why should absorbance stay below about 1.5?
Above A = 2 less than 1% of the light reaches the detector, so stray light (light of other wavelengths that leaks through) and detector noise become a large part of what is measured. The reading flattens below the true value. Dilute the sample and multiply back.
Why do I need a standard curve?
Real instruments and real solutions are not perfect, and ε for a given sample may not be known. Measuring standards of known concentration under the same conditions calibrates the instrument and checks that the response is linear; the unknown is then read off the fitted line. Only trust it within the range of the standards.
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