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Absorption of Light A spectrophotometer measures the concentration of a sample dissolved in water by shining a light through it and recording the amount of light that emerges. In other words, if we know the amount of light that is absorbed,we can calculate the concentration of the sample. For a certainsubstance the concentration (in moles per liter, mol/L) isfound by using the formula$$C=-2500 \ln \left(\frac{I}{I_{0}}\right)$$where $I_{0}$ is the intensity of the incident light and $I$ is theintensity of light that emerges. Find the concentration of thesubstance if the intensity $I$ is 70$\%$ of $I_{0}$ .
$C \approx 891.69 \mathrm{mol} / \mathrm{L}$
Algebra
Chapter 4
Exponential and Logarithmic Functions
Section 3
Logarithmic Functions
Missouri State University
McMaster University
Lectures
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So if we want to find the concentration in the problem for given the equation of concentration and we're told Dad eyes 70% of eyes, 70% of I not So this means that I is equal 2.7 of I not so we can replace I with with I'm not here. And so rewriting this problem gives us that our concentration is equal to is equal to negative. Negative 25 100 natural log of Now we have this 0.7 0.7 I not over a 0.7 I not over over one eye. Not so we have 10.7 point 7/1. So this just is. We could just say this is equal 2.7. This is equal 2.7. And so now if we want to solve this, what we have, we have negative, See over over, or we can say, let's say see, over over 2500 is equal to the negative of natural log of 0.7. So we take we take e to the e to the or we could we could just We could plug this into our calculated this way because because, um, converting this to exponential form would be the same because we would have to plug this into our calculator anyway. So if we plug this into our calculator and we say negative 2500 of the natural log of the national log of 0.7, this gives us negative. This gives a C is approximately, sees approximately 891 0.69 and so this is our solution.
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