$4-5.$ The rate at which breeding occurs in a reactor is occasionally measured in terms of

the doubling time, $t_D.$ This is defined as the time required for the amount of fissile material

in a reactor to double. Show that

$t_D=\frac{M{E}_R}{0\mathrm{.}895(1+)PAG}$

where $M$ is the original fuel inventory of the reactor in grams, $E_R$ is the recoverable

energy in MeV,$P$ is the operating power in MW$,A$ is the atomic weight of the fuel, and

$G$ is the breeding gain.