The ${?}^{233}U$ and the ${?}^{238}U$ masses in natural uranium are split between enriched and depleted streams as a result of the enrichment process. If the input masses and the output enrichments are specified, mass conversion determines the maximum $($no loss$)$ quantity of each isotope in the output streams. Considering a $1kg$ input of natural uranium, a $3wt\%{?}^{23}U$ enriched stream, and a $0\mathrm{.}3wt\%{?}^{23}U$ depleted stream:

a$.$ Calculate the masses of ${?}^{23}U,{?}^{23}U,$ and the total $U$ in each of the two output streams.

b$.$ Calculate the fraction of the initial ${?}^{235}U$ that ends up in each output stream.

c$.$ Repeat part $($b$)$ for the ${?}^{238}U$ and total $U.$