An isotope 53131I can decay by two competing processes from its initial excited state:
• With probability 0.60, the nucleus undergoes a β− decay directly to a stable ground state.
• With probability 0.40, the nucleus emits a γ photon, remaining the same nuclide but dropping to its ground state, after which it necessarily undergoes a single β− decay.
Assume that once in the ground state, the isotope always decays by exactly one β− emission and no further transitions occur.
(a) For each distinct decay path, state the daughter nuclide produced after the β− emission.
(b) Calculate the overall probability that a randomly chosen 131I nucleus will become the nuclide identified in part (a) after exactly one emission of a β− particle. Show how the branching information is incorporated.
(c) Discuss whether nucleon number, lepton number, and electric charge are conserved along each possible decay path.