From my understanding of the products of radioactive decay (alpha particles, beta particles, and gamma are all I know of), the particles (or energy I guess?) are stopped by a medium according to it's density, and the atomic size of the atoms that make it up (I could quite easily be wrong). Without conducting an experiment, how would you calculate how far the three types of radioactive decay can travel through a certain material, knowing only the material's density (or any other documentable property)?
We take into account the inelastic interactions that take place between the respective type of particle and the material, i.e. interaction that can consume part of the energy of the radiation particle, and calculate the mean-free path of the respective type of particle in the material. In this calculus we also consider the density and the structure of the material. In general, for particles with rest-mass, the higher is the velocity, the lower is the cross section of interaction with the material, and longer the free path in it. But the charge of the particle and mass are also relevant. For instance, $\alpha$ particles although very energetic, have low velocities, are highly ionizing and can travel only a few centimeters in air. The opposite example are $\gamma$ rays. The higher is their energy the harder is to stop them. Before being finally being absorbed by some photoelectric event or pair production (for energy > 1.02Mev), they can interact a lot on the way by Compton scattering. Thick walls of concrete are needed to stop them, or isolation by lead layers. $\beta$ radiation has intermediate properties.