The two dominant forces in the nucleus of an atom are the electromagnetic force, which is the repulsive force among protons, and the strong force, which is attractive among protons and neutrons. Many of the things we observe in nuclei can be explained by a balance of these forces, combined with the Pauli principle for the particles in the nucleus. For instance, most stable nuclei have somewhat more neutrons than protons, although nonmassive stable nuclei have about the same number of neutrons as protons. Nuclear physicists say that these nuclei are in a valley of stability, so that N ≥ Z, Where N is the number of neutrons and Z is the atomic number and the symbol means that N is greater than or approximately equal to Z.

When the difference N–Z is strongly positive, it is likely that a nucleus will decay by β – decay. in which a neutron converts into a proton, an electron, and an antineutrino (which rarely interacts with matter).

When N–Z is only slightly positive or even negative, then there are two likely modes of decay: β + decay and K-capture. In β + decay (also called positron decay), a proton is converted into a neutron, a positron, and a neutrino. In K-capture, an electron from an orbital of the first shell (or K-shell, that is the 1s orbital) combines with a nuclear proton to make a neutron and a neutrino. This often happens in nuclei in which positron decay is forbidden, for instance, because it is energetically unfavourable. K-capture is possible because there is some overlap of the first-shell orbital and the volume taken up by the nucleus, that is, the first-shell orbital has a non zero amplitude at the center of the nucleus.

(i) Which of the following represents the K-capture decay of 56 Ni?