Spectrophotometry Calculators

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Spectrophotometry measures how much light of a specific wavelength is absorbed or transmitted by a solution, based on Beer-Lambert law: A = ε × c × l, where A is absorbance (dimensionless), ε is the molar extinction coefficient (M⁻¹cm⁻¹), c is the concentration (M), and l is the path length (cm). A = log(I₀/I) = −log(T), where T = transmittance. In biology and chemistry, spectrophotometry is used to quantify DNA/RNA (A₂₆₀), proteins (A₂₈₀, Bradford assay at A₅₉₅, BCA at A₅₆₂), bacterial growth (OD₆₀₀), enzyme activity, and chemical concentrations.

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Beer-Lambert Law

A = ε × c × l

A = absorbance (dimensionless). ε = molar absorption coefficient (M⁻¹cm⁻¹). c = concentration (mol/L). l = path length (cm, typically 1.0 cm). Transmittance T = I/I₀; A = −log(T) = log(I₀/I). Linear range: typically A = 0.1–1.0 (above 1.0: multiple scattering; below 0.1: too low signal).

Key Wavelengths in Biology

  • A₂₆₀: DNA (50 μg/mL per unit); RNA (40 μg/mL per unit); A₂₆₀/A₂₈₀ purity check
  • A₂₈₀: proteins (aromatic residues Trp, Tyr); A₂₈₀ = ε × c for known ε
  • A₅₉₅: Bradford assay (protein quantification)
  • A₅₆₂: BCA assay (protein)
  • A₆₀₀: bacterial cell density (OD₆₀₀)
  • A₅₄₀: hemoglobin; A₄₁₀: porphyrins

Calibration Curve

Prepare standards of known concentration → measure absorbance → plot A vs. c → linear regression → use slope to calculate unknown concentrations from their absorbance readings.

Glossary

Beer-Lambert Law
A = ε × c × l; absorbance = molar extinction coefficient × concentration × path length; linear when A = 0.1–1.0; basis for all spectrophotometric quantification.
Molar Extinction Coefficient (ε)
The absorbance of a 1 M solution in a 1 cm path (M⁻¹cm⁻¹); characteristic of each molecule at each wavelength; used to calculate concentration from absorbance: c = A/(ε×l).
A260/A280 Ratio
Purity check for nucleic acid preparations; pure DNA ≈ 1.8–2.0; pure RNA ≈ 2.0; < 1.7 indicates protein or phenol contamination; measured by NanoDrop or UV spectrophotometer.

Frequently Asked Questions

Beer-Lambert law: A = ε × c × l. A = absorbance = log(I₀/I). ε = molar extinction coefficient (M⁻¹cm⁻¹) — characteristic of each molecule at each wavelength. c = molar concentration. l = path length (usually 1 cm). Limitations: Linear only in 'ideal' conditions: high concentrations → molecular interactions change ε (non-linear); solutions that scatter light (turbid samples) violate the law; fluorescent solutions; stray light in the spectrophotometer. Practical range: A = 0.1–1.0 for most instruments. Above A ≈ 1.5: dilute the sample. The law assumes monochromatic light and non-interacting solute molecules.

Nucleic acids absorb UV light at 260 nm due to the aromatic rings of nucleobases. Conversion factors: dsDNA: A₂₆₀ = 1.0 → 50 μg/mL. ssDNA: A₂₆₀ = 1.0 → 33 μg/mL. RNA: A₂₆₀ = 1.0 → 40 μg/mL. Concentration = A₂₆₀ × conversion factor × dilution factor. Purity assessment: A₂₆₀/A₂₈₀: pure DNA ≈ 1.8–2.0; pure RNA ≈ 2.0; < 1.7 indicates protein or phenol contamination. A₂₆₀/A₂₃₀ ≈ 2.0–2.2; < 1.8 indicates organic contamination (guanidine, ethanol). NanoDrop: uses a 0.1 mm path length; requires only 1–2 μL.

OD₆₀₀ (optical density at 600 nm) is used to monitor bacterial growth. At 600 nm, bacterial cells scatter light (not absorb it, technically) — the apparent absorbance is proportional to cell density. For E. coli: OD₆₀₀ = 1.0 ≈ 8 × 10⁸ cells/mL (rule of thumb; varies by strain and instrument). Growth rate (μ) = slope of ln(OD₆₀₀) vs. time during exponential phase. Linear range: OD₆₀₀ ≤ 0.3–0.4; above this, dilute and multiply by dilution factor. Always blank with uninoculated medium.

A calibration curve allows concentration to be determined from absorbance readings. Steps: Prepare standards: a series of solutions with known concentrations spanning the expected range of unknowns (including a blank at c = 0). Measure absorbance of each standard at the appropriate wavelength. Plot A (y-axis) vs. c (x-axis). Fit a linear regression: A = m × c + b; within the linear range, the y-intercept should be near zero. Calculate unknown concentrations: c_unknown = (A_unknown − b) / m. Requirements: all standards and unknowns should have the same matrix (same buffer, pH, salts) to avoid matrix effects.