It can be seen that the absorption of \(\beta\)-particles is only roughly exponential. That arises from the fact that \(\beta\)-particles are emitted from a radioisotope with a range of kinetic energies. Thus absorption coefficients determined from Beer’s law are only approximate.

The more penetrating component is due to Bremsstrahlung, electromagnetic radiation resulting from the rapid acceleration and deceleration of \(\beta\)-particles travelling through the material. Being electromagnetic in character it is less easily absorbed and hence more penetrating than the original \(\beta\)-particles.

The end-point energy of the \(\beta\)-particles can be estimated from their range \(R\) in a particular absorber. \(R\) is defined as the total thickness (\(\rho\,x\)) of absorber through which a \(\beta\)-particle of maximum energy will traverse before coming to rest. The end-point energy is related to the range by the empirical Feather relationship:

where \(E\) is in MeV and \(R\) in g cm\({}^{-2}\).