Q.55 A UV-visible spectrophotometer has a minimum detectable absorbance of 0.02.
The minimum concentration of a protein sample that can be measured reliably in this instrument with a cuvette of 1 cm path length is _______ μM.
The molar extinction coefficient of the protein is 10,000 L mol−1 cm−1.
Concept Overview
UV-Vis spectrophotometers detect protein concentrations based on the Beer-Lambert law. The lowest measurable absorbance defines the limit of detection. For an instrument with a minimum A = 0.02, 1 cm path length, and ε = 10,000 L mol⁻¹ cm⁻¹, the corresponding minimum protein concentration is 2 μM.
Beer-Lambert Law
The relationship between absorbance and concentration is:
A = ε × c × l
- A = absorbance
- ε = molar extinction coefficient
- c = concentration
- l = cuvette path length
Given Values
- Minimum absorbance, A = 0.02
- Path length, l = 1 cm
- Extinction coefficient, ε = 10,000 L mol⁻¹ cm⁻¹
Step-by-Step Calculation
Rearranging Beer-Lambert law:
c = A / (ε × l)
c = 0.02 / (10,000 × 1) = 2 × 10⁻⁶ M = 2 μM
This assumes the system remains in the linear range; below 0.02 absorbance, noise prevents accurate readings.
Result
Minimum measurable protein concentration: 2 μM
Why This Matters in Protein Analysis
Proteins absorb strongly near 280 nm due to aromatic residues. The reliable range for UV absorbance quantification is approximately 0.02–1.0 A. Lower values become unreliable due to stray light and baseline noise.
Practical Implications
- Useful for enzyme assays and purification monitoring
- At concentrations below 2 μM, alternative assays are recommended (Bradford, BCA, fluorescence)
- Dilution or microvolume cuvettes can push limits further
Exam Note
This type of question is commonly seen in biotechnology entrance exams, including GATE and IIT JAM. The expected numerical answer is 2 (μM).
