2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170562General Berry-Esseen bounds are developed for the exponential distribution using Stein's method. As an application, a sharp error term is obtained for Hora's result that the spectrum of the Bernoulli-Laplace Markov chain has an exponential limit. This is the first use of Stein's method to study the spectrum of a graph with a non-normal limit.26 pages; this is a major revision, with an additional co-author (A. Rollin) and sharp boundsProbabilityCombinatorics60C05, 60F05text