# Determining the molar extinction coefficient of gold nanoparticles

Using the data sets made available in the experimental data, students can first estimate the wavelength of maximum absorbance and then estimate the absorptivity coefficient for each nanoparticle preparation by calculating a linear regression equation based on the absorbance vs. concentration data.

Q26. At which wavelength does each nanoparticle solution exhibit the maximum absorbance? This wavelength is referred to as λmax.

Students can estimate λmax by examining Figure 6 which shows spectra recorded on nanoparticles synthesized under different pH conditions or analyzing the visible spectra provided in the experimental data. As the pH increases, a red shift is observed in agreement with increased particle size. This shift is also portrayed in Table 1 in the module.

Q27. What wavelength would you choose to quantitatively determine the concentration of the nanoparticles? Why did you choose this wavelength?

Students should answer this question by reporting λmax. This wavelength is chosen because it provides the maximum sensitivity for the determination of the concentration according to Beer’s law.

Q28. What is the value of the absorbance at λmax for each nanoparticle solution? Complete Table 5 by reporting the nanoparticle concentration from Table 4 and λmax estimated from the spectra found in the link to the experimental data.

Table 5 can be completed by inserting the nanoparticle concentrations calculated in Table 4 and by reporting the λmax derived by analyzing the visible spectra provided in the experimental data.

Q29. How could you use a plot of absorbance vs. concentration at the wavelength chosen above to determine the molar extinction coefficient of a gold nanoparticle solution?

According to Beer’s law, A = εbc, where A is the absorbance, ε is the molar extinction coefficient, b is the path length of the cuvette and c is the concentration. Thus, the molar extinction coefficient can be obtained by calculating the slope of the absorbance vs. concentration plot. Since in most instances the path length b of the cuvette is equal to 1 cm, the slope is the same value as ε.