13.1: Transmittance and Absorbance

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As light passes through a sample, its power decreases as some of it is absorbed. This attenuation of radiation is described quantitatively by two separate, but related terms: transmittance and absorbance. As shown in Figure \(\PageIndex{1}a\), transmittance is the ratio of the source radiation’s power as it exits the sample, P_T, to that incident on the sample, P₀.

\[T=\frac{P_{\mathrm{T}}}{P_{0}} \label{10.1} \]

Multiplying the transmittance by 100 gives the percent transmittance, %T, which varies between 100% (no absorption) and 0% (complete absorption). All methods of detecting photons—including the human eye and modern photoelectric transducers—measure the transmittance of electromagnetic radiation.

Schematic diagram showing the attenuation of radiation passing through a sample and a blank. — Figure \(\PageIndex{1}b\). (a) Schematic diagram showing the attenuation of radiation passing through a sample; P₀ is the source’s radiant power and P_T is the radiant power transmitted by the sample. (b) Schematic diagram showing how we redefine P₀ as the radiant power transmitted by the blank. Redefining P₀ in this way corrects the transmittance in (a) for the loss of radiation due to scattering, reflection, absorption by the sample’s container, and absorption by the sample’s matrix.

Equation \ref{10.1} does not distinguish between different mechanisms that prevent a photon emitted by the source from reaching the detector. In addition to absorption by the analyte, several additional phenomena contribute to the attenuation of radiation, including reflection and absorption by the sample’s container, absorption by other components in the sample’s matrix, and the scattering of radiation. To compensate for this loss of the radiation’s power, we use a method blank. As shown in Figure \(\PageIndex{1}b\), we redefine P₀ as the power exiting the method blank.

An alternative method for expressing the attenuation of electromagnetic radiation is absorbance, A, which we define as

\[A=-\log T=-\log \frac{P_{\mathrm{T}}}{P_{0}} \label{10.2} \]

Absorbance is the more common unit for expressing the attenuation of radiation because—as we will see in the next section—it is a linear function of the analyte’s concentration.

Example 13.1.1

A sample has a percent transmittance of 50%. What is its absorbance?

Solution

A percent transmittance of 50.0% is the same as a transmittance of 0.500. Substituting into Equation \ref{10.2} gives

\[A=-\log T=-\log (0.500)=0.301 \nonumber \]

Exercise 13.1.1

What is the %T for a sample if its absorbance is 1.27?

Answer

To find the transmittance, \(T\), we begin by noting that

\[A=1.27=-\log T \nonumber \]

Solving for T

\[\begin{align*}-1.27 &=\log T \\[4pt] 10^{-1.27} &=T \end{align*}\]

gives a transmittance of 0.054, or a %T of 5.4%.