The isotope is known to decay either by positron emission or by electron capture
PHYSICS · Multi-part · A Level · Physics · Particles and radiation · Particles and radiation
Problem
The isotope 3374As is known to decay either by positron emission or by electron capture. In a medical-imaging experiment, detectors record a large number of positrons but no characteristic K-shell X-rays that would accompany electron capture. Assume that the detector is equally efficient at registering positrons and X-rays.
Throughout any decay, assume conservation of nucleon number, electric charge, energy, and lepton number.
(a) Identify which decay pathway is dominant in this experiment and explain how the experimental evidence supports your conclusion.
(b) Write the balanced nuclear equation for the dominant decay pathway, including all emitted particles.
(c) Using conservation of energy and lepton number, justify why both positron emission and electron capture convert a proton into a neutron, yet differ in the particles released from the nucleus and detected externally.
(d) The daughter nucleus produced is germanium. Determine its atomic number and mass number, and explain whether these values would differ if electron capture occurred instead of positron emission.