Question

Compare the passage of charged and uncharged particles through matter. What are the approximate probabilities of a single charged particle achieving a path- length equal to twice its range, or of a single photon having a pathlength twice as great as the mean free path lip? (Assume the photon is totally absorbed in its first interaction.)

Answer 1

Consider the mean free path of a charged particle through that matter as and that of a photon is . The corresponding identities that they follow are and where the -s and -s represent cross-section and particle density for charged particle and photon respectively. Now, probability that they go twice as much distance as their mean free path are and similarly respectively [this is easily seen from the fact that probability that object travels macroscopic distance without interaction is ].

Once we have these, we can compare them. Their ratio comes out to be:

Now, in general a charged particle will interact only with the nucleus, whereas photons interact with electrons and the nucleus as well, thus this ratio is greater than 1 (because represents the total available cross-section, which is more for particles than photons), and hence it's more likely that a charged particle will travel twice it's mean path length rather than a photon doing the same.