Chapter 4.3, Problem 86E

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 certain substance the concentration (in moles per liter, mol/L) is found by using the formula

$C=-2500\ln \left(\frac{I}{I_0}\right)$

where I₀ is the intensity of the incident light and I is the intensity of light that emerges. Find the concentration of the substance if the intensity I is 70% of I₀.

To determine

The concentration of the substance, if the intensity I is $70\%$ of $I_0$.

Answer to Problem 86E

The concentration of the substance is $\underset{¯}{C=891.68725}$.

Explanation of Solution

The intensity of light I is given as $70\%I_0$.

Further, the substance of concentration is given as, $C=-2500\ln \left(\frac{I}{I_0}\right)$, where $I_0$ is incident of light and $I$is intensity of light that emerges.

Substitute the value of I in the above formula, $C=-2500\ln \left(\frac{I}{I_0}\right)$,

$\begin{array}{c}C=-2500\ln \left(\frac{\left(0.7\right)I_0}{I_0}\right)\\ =-2500\ln \left(0.7\right)\\ =-2500\left(-3.566749\right)\\ =891.68725\end{array}$

Hence, the concentration of the substance is $\underset{¯}{C=891.68725}$.