# Beer-Lambert Law; Fraction of hemoglobin

#### himerusandero

1. The problem statement, all variables and given/known data

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, given below, 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.

I = I010-εCL or log10(I / I0) = -εCL

The quantity ε is called the extinction coefficient, and its value depends on the frequency of the light. (It has units of m2/mol.) 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 also that 940-nm light has zero absorption (ε = 0) in oxygenated hemoglobin and 660 nm light has zero absorption in deoxygenated hemoglobin. If 31% of the energy of the red source and 80% of the infrared energy is transmitted through the blood, what is the fraction of hemoglobin that is oxygenated?

2. Relevant equations

I = I010-εCL or log10(I / I0) = -εCL

3. The attempt at a solution

I have no idea how to even approach this...this is non-calculus based physics. I know that I am solving for the concentration and that the length and e cancel out...besides that. I keep getting the same wrong answer of 24.7%.

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