Physics

Problem

Two different fissile assemblies, A and B, are compared for their rate of neutron growth. Assembly A:

k_A = 1.0007

, generation time

\tau_A = 0.10\,\text{s}

. Assembly B:

k_B = 1.50

, generation time

\tau_B = 1.0\times10^{-8}\,\text{s}

. Both assemblies start with the same initial neutron population

N_0 = 1.0\times10^{3}

. a. (i) Derive an expression for the neutron population

N(t)

as a function of time in terms of

k

\tau

and

N_0

. b. (ii) Using the expression obtained, calculate the time required for each assembly to reach a neutron population of

10^{18}

. c. (iii) Comment on the suitability of each assembly for use as (a) a controlled power reactor core and (b) an explosive device.