Dynamical effects of a solvent (environment) on an electron transfer (ET) reaction are investigated by using the Sumi-Marcus reaction-diffusion equation; this equation describes the time evolution of population distribution function of a reactant in a slow nuclear coordinate system. Assuming that viscosity of the solvent (environment) is proportional to a relaxation time scale of the slow nuclear mode, power dependence of a mean lifetime of ET on the relaxation time scale becomes the same as the one on the viscosity. Therefore, the former power dependence is investigated instead of the latter, and it is found that the power in the limit of the (infinitely) large relaxation time scale is 1-r when r < 1, and 0 when 1 less than or equal to r, where r is the ratio of the reorganization energy of fast nuclear modes to the slow nuclear mode. However, this limit cannot always be reached in a realistic situation. Therefore, the present theory is extended to a large but finite relaxation time scale. The values of the power obtained by the present theory are in reasonable agreement with the ones calculated numerically by W. Nadler and R. A. Marcus [J. Chem. Phys. 86, 3906 (1987)]. Finally, a difficulty in numerical calculations is shown. An expansion of the population distribution function in some basis set of functions is common in numerical calculations. However, the use of that finite basis set of functions which is independent of the relaxation time scale leads to a value of the power that is either zero or unity in the limit of the large relaxation time scale, and as such cannot reproduce the correct asymptotic behavior of the mean lifetime.