Fuel Burnup. $[30$ points$]$

a$.$ How many metric tons $($tonnes$)$ of $3\%$ enriched uranium are needed to

produce one gigawatt of electric power for a year? Assume that: $(1)$ all of

the ${?}^{235}U$ atoms undergo fission; $(2)200$MeV of thermal energy are released

per fission, on average; $(3)$ none of the other isotopes in the fuel undergo

fission; and $(4)$ that the plant operates at a thermal efficiency of $33\%.($Hint:

how many ${?}^{235}U$ atoms undergo fission during this time?$)[20$ points$]$

b$.$ What does the acronym GWDT$/$MTHM stand for? Explain how it is used. $[5$

points$]$

c$.$ As burnup increases, how does the composition of the nuclear fuel change?

Explain how this impacts criticality using the $4-$factor formula. $[5$ points$]$