# Operation of the pulse oximeter (see previous problem ). 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 − ∈ C L or log 10 ( I I 0 ) = − ∈ C L 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 m 2 /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 940-nm light has zero absorption ( ∈ = 0) in oxygenated hemoglobin and 660-nm light has zero absorption in deoxygenated hemoglobin. If 33% of the energy of the red source and 76% of the infrared energy is transmitted through the blood, what is the fraction of hemoglobin that is oxygenated?

### College Physics

11th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305952300
Chapter 21, Problem 54P
Textbook Problem
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## Operation of the pulse oximeter (see previous problem). 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 − ∈ C L or log 10 ( I I 0 ) = − ∈ C L 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 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 940-nm light has zero absorption (∈ = 0) in oxygenated hemoglobin and 660-nm light has zero absorption in deoxygenated hemoglobin. If 33% of the energy of the red source and 76% of the infrared energy is transmitted through the blood, what is the fraction of hemoglobin that is oxygenated?

To determine
Fraction of hemoglobin oxygenated.

### Explanation of Solution

Explanation

Given Info:

The formula to calculate the percentage of radiation transmitted is

log10(II0)=εCL

• C is the concentration of the solution through which light is transmitting,
• ε is the extinction co-efficient,
• L is the length of the solution,

Rewrite the above equation in terms of C.

C=(log10(I/I0)εL)

The formula to calculate concentration of the oxygenated hemoglobin if 33% of the red source transmitted is

Coxy=(log10(Ioxy/I0)εL)

• Coxy is the concentration of the hemoglobin oxygenated

33% of the energy of the red source transmitted through the blood. So,

Ioxy/I0=33%=0.33

Substitute 0.33 for Ioxy/I0 in the above expression to find concentration of the oxygenated hemoglobin Coxy .

Coxy=(log10(0.33)εL) (I)

The formula to calculate concentration of the deoxygenated hemoglobin if 76% of the red source transmitted is

Cdeoxy=(log10(Ideoxy/I0)εL)

• Cdeoxy is the concentration of the hemoglobin deoxygenated

76% of infra red energy is transmitted through the blood

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