11.7 Exercise 16

The intensity of cosmic ray radiation decreases rapidly with increasing energy, but there are occasionally extremely energetic cosmic rays that create a shower of radiation from all the particles they create by striking a nucleus in the atmosphere. Suppose a cosmic ray particle having an energy of $10^{10} \text{GeV}$ converts its energy into particles with masses averaging $200 \text{MeV}/ c^{2}$.

(a) How many particles are created? (b) If the particles rain down on a $1 .\text{00}-\text{km}^{2}$ area, how many particles are there per square meter?