GATE 2025 BT Q.60: solution and answer

GATE 2025 · BTQ.60 · 2 marks · NAT

The percentage of light that would pass through a sample with an absorbance of 2 would be ______% . (Round off to the nearest integer)

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Answer and solution

ANSWER

The percentage of light transmitted through a sample with absorbance 2 is 1%.

Official answer: 1Source: Official answer key, GATE 2025 BT (IIT Roorkee)

Absorbance (A) and transmittance (T) are related by $A = - lo g_{10} (T)$ , where $T$ is the fraction of incident light transmitted (0 to 1).
Rearranging: $T = 1 0^{- A}$ .
Substitute $A = 2$ : $T = 1 0^{- 2} = 0.01$ .
Percentage transmittance $= T \times 100 = 0.01 \times 100 = 1%$ .
Rounded to the nearest integer: $1%$ .

KEY IDEA

Absorbance and percentage transmittance are related by $A = - lo g_{10} (T)$ , where $T$ is the fraction (0 to 1) of incident light transmitted; percentage transmittance is $T \times 100$ .

WATCH OUT FOR

Confusing absorbance with percentage absorbed directly (e.g. assuming $A = 2$ means 2% or 98% transmittance), instead of using the logarithmic relation $T = 1 0^{- A}$ .

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GATE 2025 BT Q.60: solution and answer

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