What is the effect of the wavelength on the spectrophotometric measurements of protein? Does the wavelength setting affect the absorbance reading of a spectrophotometer? For example, if I am using a spectrophotometer at 550 nm to determine the protein concentration of my samples, would my results be different if I analyze them at 500 nm?

In addendum, keeping the wavelength around the absorption maximum for the light-attenuating species avoids introducing error into Beer's Law. There are limitations to the law, outlined here where we can see that around the lambda max, there's little change in absorption per unit wavelength:

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In case B, this would end up returning a bad extinction coefficient! You can experimentally determine this point either by testing the solution at different wavelengths or more accurately, running a program where the machine goes through it's entire wavelength range and measures absorption for you. You'll get a parabola where the maximum is your lambda max, so it's solvable by calculating the maxima if necessary (take the first derivative, set y'= 0, solve for y when x = (y'=0) for the associated ordered pair). You also want to be careful when you're using something like the Bradford assay where the bound form of the dye shifts the lambda max!