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$$ SERCP$1221\mathrm{.}11.$P$\mathrm{.}054.$MI$.$

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A "pulse oximeter" operates by using light and a photocell to measure oxygen saturation in arterial blood. The transmission of light energy as it passes through a solution of light$-$absorbing molecules is described by the Beer$-$Lambert law

$I=I_0{10}^{-CL}orlo{g}_{10}(\frac{\text{I}}{I_0})=-CL$

which gives the decrease in intensity I in terms of the distance $L$ the light has traveled through a fluid with a concentration $C$ of the light$-$absorbing molecule. The quantity $$ is called the extinction coefficient, and its value depends on the frequency of the light. $($It has units of $\frac{m^2}{m}ol.)$ Assume the extinction coefficient for $660-nm$ light passing through a solution of oxygenated hemoglobin is identical to the coefficient for $940-nm$ light passing through deoxygenated hemoglobin. Also assume that $940-nm$ light has zero absorption $(=0)$ in oxygenated hemoglobin and $660-nm$ light has zero absorption in deoxygenated hemoglobin. If $35\mathrm{.}0\%$ of the energy of the red source and $71\mathrm{.}7\%$ of the infrared energy is transmitted through the blood, what is the fraction of hemoglobin that is oxygenated?

$100$

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