Green fluorescent protein (GFP) and variants of this protein have been developed for in vivo FRET studies (Pollok B. and Heim R. Trends in Cell Biology 9 (1999): 57). Two variants of GFP, cyan fluorescent protein (CFP) and yellow fluorescent protein (YFP), form a FRET pair where R0 = 4.72 nm. The excited-state lifetime of the CFP donor in the absence of YFP is 2.7 ns.

a. At what distance will the rate of energy transfer be equal to the excited-state decay rate for isolated CFP, equal to the inverse of the excited-state lifetime?

b. Determine the distance at which the energy transfer rate will be five times the excited-state decay rate.