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The radiation effects on unsteady flow of a viscous incompressible fluid past an exponentially accelerated infinite isothermal vertical plate with uniform mass diffusion is considered in the presence of magnetic field and heat source. The governing partial differential equations are converted into a non-dimensional form and solved numerically by applying a Crank-Nicholson type of implicit finite difference method with a tri-diagonal matrix manipulation and an iterative procedure. The profiles of unsteady velocity, temperature and concentration are shown graphically for different values of thermo physical parameters. Also, the simulated values of the skin-friction coefficient, Nusselt number and Sherwood number are presented. This model finds applications in solar energy collection systems, geophysics and astrophysics, aero space and also in the design of high temperature chemical process systems.