GATE BT 2019 • Q55 NAT • 2 Marks

Section 2: General Biotechnology

Biomolecules, enzyme kinetics

Subtopic: Fundamentals of Biomolecules, enzyme kinetics

Question Statement:

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 1s uM. The molar extinction coefficient of the protein is 10,000 L mol' cm'.

Official Answer Key:

2 to 2

Step-by-Step Solution & Explanation

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2019 Q.55)** **1. Governing Concept & Definition**: - **Topic**: Biophysical Spectroscopy & Beer-Lambert Law - Absorbance $A$ is related to molar extinction coefficient ($\epsilon$), path length ($l$), and molar concentration ($C$) by: $A = \epsilon \cdot C \cdot l \implies C = \frac{A}{\epsilon \cdot l}$ **2. Detailed Step-by-Step Calculation**: - **Given**: - Minimum detectable absorbance $A_{\min} = 0.02$ - Cuvette path length $l = 1\text{ cm}$ - Molar extinction coefficient $\epsilon = 10,000\text{ M}^{-1}\text{cm}^{-1} = 10^4\text{ M}^{-1}\text{cm}^{-1}$ - **Minimum Detectable Concentration**: $C_{\min} = \frac{0.02}{10^4 \times 1} = 2 \times 10^{-6}\text{ M} = 2\text{ }\mu\text{M}$ **3. Final Answer**: - **Calculated Value**: **2 µM** - **Official GATE Accepted Range**: **2 to 2**

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test