The basicity of alkaline-exchanged zeolites (Li+, Na+, K+, Rb+, and Cs+) has been studied using a local descriptor of reactivity defined in terms of the density of states for an arbitrary bandwidth. This is the first report where a local reactivity index is evaluated through a scheme of the density of states in a cluster model of exchanged zeolite. We have found that this empirical model assesses well the experimental basicity trend of zeolites, and it gives a better description of basicity than the frontier-orbital-based approximations for the Fukui function and local softness or Mulliken population analysis. We discuss the relationship between this empirical index and the local softness defined as the local density of states evaluated at the Fermi level introduced by Yang and Parr [Proc. Natl. Acad. Sci. U.S.A. 82, 6723 (1985)].