The following questions concern the relative concentration uncertainty in spectrophotometry.
(a) If the relative concentration uncertainty is given by Equation 13-13, use calculus to show that the minimum uncertainty occurs at 36.8% T. What is the absorbance that minimizes the concentration uncertainty? Assume that ST is independent of concentration.
(b) Under shot-noise-limited conditions, the relative concentration uncertainty is given by Equation 13-14. Another form of the equation for the shot-noise limited case is12
where k is a constant. Use calculus and derive the transmittance and absorbance that minimize the concentration uncertainty.
(c) Describe how you could experimentally determine whether a spectrophotometer was operating under Case I, Case II, or Case III conditions.