Q.57 A protein solution of 1 μM has transmission of 40 % at 280 nm, when measured in
a 1 cm cuvette using a UV–Visible spectrophotometer. The transmission of the same
solution, when measured using a 2 cm cuvette is _______ %. (rounded off to the
nearest integer)
Key Answer
The transmission drops to 16% in the 2 cm cuvette due to doubled path length, following the Beer-Lambert law. This numerical answer applies Beer’s law principles central to UV-Vis spectrophotometry in protein analysis at 280 nm.[conversation_history:5]
Step-by-Step Solution
Transmission (T) measures light passing through a sample, expressed as a decimal fraction or percentage. For the 1 μM protein solution in a 1 cm cuvette, T = 40% = 0.40. Absorbance (A) converts via A = -log₁₀(T), yielding A₁ = -log₁₀(0.40) = 0.398 for path length l₁ = 1 cm.[conversation_history:5]
Beer-Lambert law states A = εcl, where ε is the molar absorptivity (constant at fixed wavelength and concentration) and c = 1 μM remains unchanged. Doubling path length to l₂ = 2 cm doubles absorbance: A₂ = 2 × A₁ = 0.796. New transmission becomes T₂ = 10^{-A₂} = 0.16, or 16%.[conversation_history:5]
Rounding 16.0 to the nearest integer gives 16, matching CSIR NET-level quantitative biochemistry problems on spectrophotometer measurements.[memory:2]
Core Concepts
Proteins absorb UV light strongly at 280 nm due to aromatic residues like tryptophan and tyrosine, enabling concentration measurements via UV-Vis spectrophotometry. This protein solution transmission problem tests Beer-Lambert law application: a 1 μM solution shows 40% transmission in a 1 cm cuvette—what’s it in a 2 cm cuvette?[conversation_history:5]
- Transmission (T): Fraction of incident light (I₀) passing through (I/I₀), often as %T.
- Absorbance (A): A = -log₁₀(T) = εcl, linear with path length (l).
- At 280 nm, proteins yield reliable A for quantification without dyes. Doubling l halves T exponentially.[memory:4]
Detailed Calculation
Convert 40% T to decimal: T₁ = 0.40.
Compute A₁: A₁ = -log₁₀(0.40) ≈ 0.398.
For 2 cm: A₂ = A₁ × (2/1) = 0.796.
T₂ = 10-0.796 = 0.16 (16%). Rounded integer: 16.[conversation_history:5]
| Cuvette Path Length | Transmission (%) | Absorbance (A) |
|---|---|---|
| 1 cm | 40 | 0.398 |
| 2 cm | 16 | 0.796 |
Exam Relevance
CSIR NET Life Sciences candidates encounter such UV-Visible spectrophotometer queries in biochemistry units. Practice verifies path length impacts without altering concentration or ε. Common pitfalls: linear T scaling (wrong) vs. logarithmic A (correct).[memory:3]
This aligns with your CSIR NET preparation in protein chemistry and spectrophotometry.[memory:2]
