Calculate the \(k\)-eff of natural uranium sphere of infinite radius, and density \(19 \mathrm{~g} / \mathrm{cc}\). Given \(\bar{u}\left(\mathrm{U}^{235}ight)=2.5 ; \sigma_{f}\left({ }^{235} \mathrm{U}ight)=600 \mathrm{~b} ; \sigma_{c}\left({ }^{235} \mathrm{U}ight)=100 \mathrm{~b}, \sigma_{f}\left({ }^{238} \mathrm{U}ight)=0 \mathrm{~b} ; \sigma_{c}\left({ }^{238} \mathrm{U}ight)=3 \mathrm{~b}\). Composition \({ }^{235} \mathrm{U} /{ }^{238} \mathrm{U}=0.7 / 99.3\).

\(\Delta=M-A\) is the "mass excess," where \(M\) is the mass of a nuclide and \(A\) its mass number. These data are given in the Nuclear Wallet cards, and elsewhere. The data given below may be useful in solving some of the problems.

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Nuclide n H 2H 4He 23 Na 24Na A (MeV) 8.071 7.289 13.136 2.425 -9.530 -8.418 56Fe -60.601 Nuclide 231 Th 232 Th 235U 236U 238U A (MeV) 33.811 35.444 40.914 42.441 47.304