The homogenous core of a thermal reactor consists of a spherical core with a radius of $150cm.$ The core

contains $U{O}_2$ fuel with a density of $10\mathrm{.}5\frac{g}{c}{m}^3.$ The uranium in the fuel is enriched to $20$ atom$-$percent

in ${?}^{235}U.$ The remainder of the fuel is ${?}^{238}U.$ Assuming $200$MeV is released for each fission event in the fuel,

calculate the thermal power generated by the reactor core when the average thermal flux is $1\mathrm{.}5x$

${10}^{12}$ neutrons $c{m}^{-2}{s}^{-1}.$