GATE 2019 BT Q.45: solution and answer

Official answer: 2Source: Official answer key, GATE 2019 BT (IIT Madras)

1. Beer-Lambert law: $A=\epsilon cl$, where $A$ is absorbance, $\epsilon$ is the molar extinction coefficient, $c$ is concentration, and $l$ is the path length.

2. Given: minimum detectable absorbance $A=0.02$, $\epsilon =10,000{\text{L mol}}^{-1}{\text{cm}}^{-1}$, $l=1\text{cm}$.

3. Rearranging for concentration: $$c=\frac{A}{\epsilon l}$$

4. Substituting the values: $$c=\frac{0.02}{10000\times 1}=2\times 10^{-6}{\text{mol L}}^{-1}$$

5. Converting to $\mu M$ (since $1{\text{mol L}}^{-1}=10^6\mu M$): $$2\times 10^{-6}{\text{mol L}}^{-1}=2\mu M$$

6. So the minimum concentration that can be measured reliably is $2\mu M$.