We study the initial-value problem for the linear Maxwell-Boltzmann equation in the whole space, by supposing that the collision frequency and the integral operator are unbounded (rigid spheres; pure scatterer). Using the theory of the linear semigroups, we show that this problem has one and only one strong solution for any suitable initial datum. We finally show that the solution is non-negative if the initial datum is non-negative and that mass conservation holds.