(a) Example 38.6 explains that the number of fission events in a chain reaction increases by a factor k with each generation. Show that the total number of fission events in n generations is N = (kⁿ⁺¹ – 1)/(k – 1).
(b) In a typical nuclear explosive, k is about 1.5 and the generation time is about 10 ns. Use the result from (a) to calculate the time for all the nuclei in a 10-kg mass ²³⁵U to fission.