Calculate the number of neutrons present after $200$ generations for a critical reactor, a

reactor with $k_{\text{e}\text{f}\text{f}}=0\mathrm{.}990,$ and a reactor with $k_{\text{e}\text{f}\text{f}}=1\mathrm{.}0001$ assuming $5**{10}^{12}\frac{\text{n}\text{e}\text{u}\text{t}\text{r}\text{o}\text{n}\text{s}}{c{m}^3}$ are

present at time $0.$ What is the reactivity in each cases in $\frac{k}{k}$ and in $pcm?$

a$)$ Critical reactor: $k_{\text{e}\text{f}\text{f}}=$

b$)$ Subcritical reactor: $k_{\text{e}\text{f}\text{f}}=$

c$)$ Supercritical reactor: $k_{\text{e}\text{f}\text{f}}=$