$(4)[15$ points$]$ Consider a mixture with the following properties:

u $\_(()$th$)(\backslash$Sigma $\_($f$,$th$))/(\backslash$Sigma $\_($a$,$th$))=1\mathrm{.}25$

L$\_($th$)^(2)=20$cm$^(2)$

p$($ res. esc. prob. $)=0\mathrm{.}8$

$\backslash$epsi lon$($ fast$-$fission factor $)=1\mathrm{.}21$

Design a reactor size and shape that would be critical if made of this material and surrounded

by vacuum. For purposes of this exercise, assume that P$\_($FNL$)=$P$\_($TNL$)$B$\_($g$)^(2)$ that will give P$\_($FNL$)$P$\_($TNL$)$ the right value to make k$\_($cff$)=1,$ then find some

size and shape that produces this B$\_($g$)^(2).$