Let each fission event in a chain reaction give rise on average to neutrons that in…

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Let each fission event in a chain reaction give rise on average to

k

neutrons that in turn cause further fission. (i) Show that the number of neutrons after

n

generations is

N_n = N_0 k^{\,n}

, where

N_0

is the initial number of neutrons. (ii) Using the result, write the conditions on

k

for (a) a steady, (b) a dying out, and (c) a rapidly growing chain reaction.