Question

An optical density of 1.0 is obtained for a solution using spectrophotometer. Which of the following interpretation can be made from this observation?

• A. The 10% of the incident light is absorbed
• B. The 90% of the incident light is absorbed
• C. The 100% of the incident light is absorbed
• D. The 100% of the incident light is transmitted

Hint:

Easy Benchmarks to Memorize:
$A = 0 \rightarrow 100\%$ Transmitted ($0\%$ Absorbed)
$A = 1 \rightarrow 10\%$ Transmitted ($90\%$ Absorbed)
$A = 2 \rightarrow 1\%$ Transmitted ($99\%$ Absorbed)
Each unit increase in Absorbance represents a 10-fold reduction in light passing through.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Optical Density (OD), also known as Absorbance ($A$), is a measure of how much light is blocked by a solution. The question asks to translate a numerical absorbance value into a percentage of light absorbed or transmitted.
Key Formula or Approach:
The relationship between Absorbance ($A$) and Percentage Transmission ($\%T$) is logarithmic:
\[ A = \log_{10} \left( \frac{100}{\%T} \right) \]
Which can be rearranged as:
\[ A = 2 - \log_{10}(\%T) \]

Step 2: Detailed Explanation:

• Calculating Transmission: Given that $A = 1.0$, substitute this into the formula:
\[ 1.0 = 2 - \log_{10}(\%T) \]
\[ \log_{10}(\%T) = 2 - 1 = 1 \]

• Solving for $\%T$: Taking the antilog (base 10) of both sides:
\[ \%T = 10^1 = 10\% \]
This means that only $10\%$ of the incident light passes through the solution and reaches the detector.

• Calculating Absorption: By principle, Light Absorbed + Light Transmitted = $100\%$ (ignoring scattering).
\[ \text{\% Absorbed} = 100\% - \text{\% Transmitted} \]
\[ \text{\% Absorbed} = 100\% - 10\% = 90\% \]

• Conclusion: An absorbance of $1.0$ indicates that the sample is quite opaque, blocking nine-tenths of the incoming light.

• Verification for other values: If $A=0$, $T=100\%$. If $A=2$, $T=1\%$.

Step 3: Final Answer:
An optical density of $1.0$ corresponds to $10\%$ transmission, which implies that $90\%$ of the incident light has been absorbed by the sample.