Of the four assumptions made in Problem 8B.2, the last two are questionable. Suppose that the first two assumptions are still reasonable and that you have at your disposal a supply of myoglobin, a suitable buffer in which to suspend the protein, ¹²C¹⁶O, ¹³C¹⁶O, ¹²C¹⁸O, ¹³C¹⁸O, and an infrared spectrometer. Assuming that isotopic substitution does not affect the force constant of the C=O bond, describe a set of experiments that:

(a) Proves which atom, C or O, binds to the haem group of myoglobin, 

(b) Allows for the determination of the force constant of the C=O bond for myoglobin bound carbon monoxide.

Data in  Problem 8B.2,

Carbon monoxide binds strongly to the Fe²⁺ ion of the haem group of the protein myoglobin. Estimate the vibrational frequency of CO bound to myoglobin by using the data in Problem 8B.1 and by making the following assumptions: the atom that binds to the haem group is immobilized, the protein is infinitely more massive than either the C or O atom, the C atom binds to the Fe²⁺ ion, and binding of CO to the protein does not alter the force constant of the C=O bond.