Beach sand mineral, monazite, is a rich source of thorium, available in large quantities in the state of Kerala in india. A typical monazite sample contains about 9% ThO_(2) and 0.35% U_(3)O_(8).^(208)Pb and ^(206)Pb are the stable end-products in the redioactive decay series of ^(232)Th and .^(238)U, respectively. All the lead (Pb) found in monazite is of radiogenic origin. The isotopic atom ratio ^(208)Pb//^(232)Th and .^(238)U are 1.41xx10^(10) years and 4.47xx10^(9) years, respectively. Assume that ^(208)Pb, ^(232)Th and .^(238)U remained entirely in the monazite sample since the formation of monazite mineral. Thorium- 232 is a fertile material for nuclear energy. In thermal neutron irradiation, it absorbs a neutron and the resulting isotope forms ^(233)U by successive beta-decays. Write the nuclear reactions for the formation of ^(233)U from ^(232)Th. In nuclear fission of ^(233)U a complex mixture of radioactive decay as shown below: _(42)^(101)Mo underset(t_(1//2)=14.6 min)(rarr)_(43)^(101)Tc underset(t_(1//2)=14.3 min)(rarr)_(44)^(101)Ru