Cooling time of CR in the ICM as a function of their kinetic energy. Left: CRe cooling times for typical densities and magnetic field strength that range from the central to the peripheral regions in galaxy clusters. Coulomb and IC/synchrotron cooling is modeled following Gould (1972b) and Rybicki & Lightman (1979), respectively. Right: CRp cooling times for the same densities. Coulomb cooling is modeled following Gould (1972a). The hadronic cooling time above the kinematic threshold for pion production is τ_pp = 1/(0.5   σ_pp   n_N   υ_CR) with σ_pp = 32   mbarn, an inelasticity of  ~50% and υ_CR the CRp velocity. It is apparent that CRp above 10 GeV have livetimes in the ICM at least 60 times longer than CRe at any energy. CRe can survive for a Hubble time without re-acceleration only within the dilute outskirts of clusters. The radio emitting electrons have an energy of about 10   GeV in μG fields, and therefore a lifetime of 0.1 Gyr or less. If they are of hadronic origin, their parent CRp had energies of about 100 GeV, which have considerable longer lifetimes.