Consider a Rutherford scattering experiment in which an alpha particle is fired at a sheet of atoms only one atomic layer thick (Fig. P29.3). The radius of an alpha particle is about 1 fm (1x10^-15 m) and assume the radius of the nuclei in Figure P29.3 has the same value. Also assume the spacing between atoms in the sheet is 0.3 nm. 

(a) If alpha particles are fired at random at the sheet, what is the probability that one will strike a nucleus? 

(b) If one trillion (10¹²) alpha particles are fired, about how many will hit a nucleus?