Compute the following reaction rates \(/ \mathrm{cm}^{3} / \mathrm{s}\) :

a. B-10(n, \(\alpha) \mathrm{Li}-7\) in the material Boron Carbide \(\mathrm{B}_{4} \mathrm{C}\) of density \(2.3 \mathrm{~g} / \mathrm{cc}\) : Take the cross-section to be \(500 \mathrm{~b}\), flux as \(10^{15} \mathrm{n} / \mathrm{cm}^{2} / \mathrm{s}\) and abundance of \(\mathrm{B}-10\) as \(20 \%\). If the material is exposed to 100 days of neutron flux, how much Li-7 gets produced in grams.

b. Fe-54(n,p)Mn-54 in the material Iron of density \(7.86 \mathrm{~g} / \mathrm{cc}\). Take the cross-section to be \(25 \mathrm{mb}\) and flux to be \(10^{14} \mathrm{n} / \mathrm{cm}^{2} / \mathrm{s}\). Calculate the activity of Mn-54 assuming its halflife to be 312 days.