In this paper, we investigate the physics of the positron annihilation process, which occurs in a PET imaging system. In particular, the diffusion of beta particles (positrons) within water was addressed. Beta particles are emitted isotropically from the same source point with random directions and randomly chosen energy levels. After traversing a certain distance within water, beta particles lose a certain amount of its energy. The inelastic collisions with atomic electrons are mainly responsible for the energy dissipation of charged particles, such as electrons and positrons (that have low mass). The energy loss rate due to inelastic process is estimated by using the Beta-Bloch formula. These results help in understanding how to develop and implement a computationally efficient Monte Carlo Simulation of the positron annihilation process.