In passing through matter, fast charged particles ionize the atoms or molecules which they encounter. Thus, the fast particles gradually loose energy in many small steps. By stopping power we mean the average energy loss of the particle per unit path length, measured for example in MeV/cm. The stopping power depends on the type and energy of the particle and on the properties of the material it passes. Since the production of an ion pair (usually a positive ion and a (negative) electron) requires a fixed amount of energy (for example, 33 eV in air), the density of ionisation along the path is proportional to the stopping power of the material.
By 'stopping power', we mean a property of the material, while 'energy loss per unit path length' describes what happens to the particle. But numerical value and units are identical for both quantities; they are usually written with a minus sign in front: -dE/dx, where E means energy, and x is the path length.
The stopping power and hence, the density of ionization, usually increases toward the end of range and reaches a maximum, the Bragg Peak, shortly before the energy drops to zero. This is of great practical importance for radiation therapy.
The picture shows how the stopping power of 5.49 MeV alpha particles increases while the particle traverses air, until it reaches the maximum. This particular energy corresponds to that of the naturally radioactive gas radon (radon-222) which is present in the air wherever the ground contains granite.
The range can be calculated by integrating the reciprocal stopping power over energy.