The radiative lifetime of the AΠ1/22 (v=0) state in radium monofluoride (RaF) is measured to be 35(1) ns. The lifetime of this state and the related decay rate Γ=2.86(8)×107 s-1 are of relevance to the laser cooling of RaF via the optically closed AΠ1/22←Xς1/22 transition, which makes the molecule a promising probe to search for new physics. RaF is found to have a comparable photon-scattering rate to homoelectronic laser-coolable molecules. Owing to its highly diagonal Franck-Condon matrix, it is expected to scatter an order of magnitude more photons than other molecules when using just three cooling lasers, before it decays to a dark state. The lifetime measurement in RaF is benchmarked by measuring the lifetime of the 8P3/2 state in Fr to be 83(3) ns, in agreement with literature.