We study the spontaneous emission of a single emitter close to a metallic nanoparticle, with the aim to clarify the distance dependence of the radiative and nonradiative decay rates. We derive analytical formulas based on a dipole-dipole model, and show that the non-radiative decay rate follows a $R^{-6}$ dependence at short distance, where $R$ is the distance between the emitter and the center of the nanoparticle, as in Försters energy transfer. The distance dependence of the radiative decay rate is more subtle. It is chiefly dominated by a $R^{-3}$ dependence, a $R^{-6}$ dependence being visible at plasmon resonance. The latter is a consequence of radiative damping in the effective dipole polarisability of the nanoparticle. The different distance behavior of the radiative and non-radiative decay rates implies that the apparent quantum yield always vanishes at short distance. Moreover, non-radiative decay is strongly enhanced when the emitter radiates at the plasmon-resonance frequency of the nanoparticle.