Prepare a set of suspensions of the particles of known concentrations. Measure their absorbance spectra. Choose the wavelength you wish to monitor (typically the wavelength with the highest absorbance). Make a plot of absorbance at that wavelength versus concentration, using only those concentrations in the linear range. The slope of the line is the extinction coefficient. The extinction coefficient also takes into account the pathlength, which is the distance the light passes through the sample, defined by the dimensions of the cuvette. (Most cuvettes have a pathlength of 1 cm.) Thus, the units of the extinction coefficient are absorbance units (which is actually unitless) divided by concentration and pathlength. For UV measurements, you should use a quartz cuvette because glass and plastic absorb in the UV. Something else to consider is that the apparent absorbance of nanoparticles will include (and may be dominated by) a contribution from light scattering (turbidity) rather than actual absorbance.
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