 Solution

At this point $N_{\mathrm{Th}}/N_{Th0}=0.95$, so $a\Phi =-\ln 0.95$ and $e^{-b\Phi }=0.95^{b/a}=0.345671$. The solution from part (c) givesThereforeThe fissile population has declined by about $4.51\%$ from its initial value, while the conversion ratio has decreased slightly from $0.9595$. The replacement shortfall persists over this interval. Maintaining a specified long-term fuel inventory would require replenishment or a different balance of reactions; the prescribed-flux equations alone do not establish a constant-power operating state. Intermediate decay delays and the changing neutron spectrum were excluded by the original lumped model.