The element number of Fe is 26, which means that the number of neutrons of the following isotopes is:
53-Fe: 27
54-Fe: 28
56-Fe: 30
57-Fe: 31
58-Fe: 32
59-Fe: 33
Because 53-Fe has too few neutrons when compared to the other isotopes we can rule out any decay that involves losing a neutron: (alpha decay, beta decay) So, this isotope will prefer to decay by electron capture or positron emission (assuming the system has about 1 MeV to spare), but in each case the product will be the same: 53-Mn (long-lived radioisotope).
