Answer : The correct option is, (C)
![^(58)\textrm{Fe}](https://img.qammunity.org/2020/formulas/chemistry/college/xcnzlhjjyv34b2j7wrzthlyw48sejjqcah.png)
Explanation :
Neutron capture : In this decay process, an atomic nucleus and one or more number of neutrons collide and combine to form a heavier nucleus. The mass number changes in this process.
The neutron capture equation is represented as,
![_Z^A\textrm{X}+_(0)^1\textrm{n}\rightarrow _(Z)^(A+1)\textrm{X}+\gamma](https://img.qammunity.org/2020/formulas/chemistry/college/zcaqxj0poypvwqy2txo59atkhzkklkjnqp.png)
(A is the atomic mass number and Z is the atomic number)
Beta emission or beta minus decay : It is a type of decay process, in which a neutrons gets converted to proton, an electron and anti-neutrino. In this the atomic mass number remains same.
The beta minus decay equation is represented as,
![_Z^A\textrm{X}\rightarrow _(Z+1)^A\textrm{Y}+_(-1)^0e](https://img.qammunity.org/2020/formulas/chemistry/college/j58yxub4kyhxdjcnnmz70um4blot4gtgfi.png)
(A is the atomic mass number and Z is the atomic number)
As per question, the cobalt-60 is produced by a three reaction process involving neutron capture, beta-emission, and neutron capture.
Process 1 : Neutron capture.
![_(26)^(58)\textrm{Fe}+_(0)^1\textrm{n}\rightarrow _(26)^(59)\textrm{Fe}+\gamma](https://img.qammunity.org/2020/formulas/chemistry/college/miknk1dutza65gj6f8gg5zz4ay9p2lmpx0.png)
Process 2 : Beta emission.
![_(26)^(59)\textrm{Fe}\rightarrow _(27)^(59)\textrm{Co}+_(-1)^0e](https://img.qammunity.org/2020/formulas/chemistry/college/35a9mfgxm1ib1o00rg9yuwpn5arkeb0fqu.png)
Process 3 : Neutron capture.
![_(27)^(59)\textrm{Co}+_(0)^1\textrm{n}\rightarrow _(26)^(60)\textrm{Co}+\gamma](https://img.qammunity.org/2020/formulas/chemistry/college/ibw3ui7chpf3ohtjabcc5bn95elybl46hs.png)
From this we conclude that, the initial reactant in the production of cobalt-60 is
![_(26)^(58)\textrm{Fe}](https://img.qammunity.org/2020/formulas/chemistry/college/ughbiiumn30bm3wcv1p5krxllz4j4xl00q.png)
Hence, the correct option is, (C)
![^(58)\textrm{Fe}](https://img.qammunity.org/2020/formulas/chemistry/college/xcnzlhjjyv34b2j7wrzthlyw48sejjqcah.png)