It is well known that the Classical theory of the electron reachedthe limits of its description at time intervals of the order of 10^-23 secs, that is the Compton time. It is widely believed that below these timeintervals Classical Electrodynamics doesn't work and that a Quantumdescription is required. Using the Lorentz Dirac and the Dirac equa-tions of the electron, we point out that in fact there is a convergenceof the two descriptions at the Compton scale.