Question

{"given":"Four nuclear reaction equations are given. We must identify which one represents $\\gamma$-decay.","key_observation":"In $\\gamma$-decay, an excited nucleus de-excites by emitting a gamma photon ($\\gamma$). Both the mass number $A$ and atomic number $Z$ remain unchanged during this process.","option_analysis":[{"label":"(A)","text":"$^{A}_{Z}X + \\gamma \\rightarrow ^{A}_{Z-1}X + a + b$","verdict":"incorrect","explanation":"The atomic number changes from $Z$ to $Z-1$, so this is not $\\gamma$-decay. This appears to represent a photo-nuclear reaction where $\\gamma$ is absorbed as a reactant, not emitted."},{"label":"(B)","text":"$^{A}_{Z}X + ^{1}_{0}n \\rightarrow ^{A-3}_{Z-2}X + c$","verdict":"incorrect","explanation":"Both mass number ($A \\rightarrow A-3$) and atomic number ($Z \\rightarrow Z-2$) change, so this is not $\\gamma$-decay. This represents a neutron-induced nuclear reaction."},{"label":"(C)","text":"$^{A}_{Z}X^{*} \\rightarrow ^{A}_{Z}X + \\gamma$","verdict":"correct","explanation":"Both $A$ and $Z$ remain unchanged while a gamma photon $\\gamma$ is emitted, which is the defining characteristic of $\\gamma$-decay. The nucleus simply transitions from an excited state to a lower energy state."},{"label":"(D)","text":"$^{A}_{Z}X + e^{-} \\rightarrow ^{A}_{Z-1}X + g$","verdict":"incorrect","explanation":"The atomic number changes from $Z$ to $Z-1$, so this is not $\\gamma$-decay. This represents electron capture (a type of $\\beta$-decay), where an orbital electron is absorbed by the nucleus."}],"answer":"(C)","formula_steps":[]}