Structural changes in proteins have been measured using FRET with the amino acid tryptophan as the donor and dansyl as the acceptor, where dansyl is attached to the protein through addition to amino acids with aliphatic amine groups such as lysine. For this pair R₀ = 2.1 nm, and the excited-state lifetime of tryptophan is ∼1.0 ns. Determine the rate of energy transfer for r = 0.50, 1.0, 2.0, 3.0, and 5.0 nm.