Final answer:
The correct decay mode in proton-rich nuclei is positron emission. This occurs when a proton in the nucleus is transformed into a neutron, releasing a positron.
Step-by-step explanation:
In proton-rich nuclei, the common decay mode is positron emission (also known as beta-plus decay). This type of radioactive decay occurs when a proton in the nucleus is transformed into a neutron and a positron, which is the antiparticle or antimatter counterpart of the electron.
This process is a manifestation of the weak nuclear force and ensures that charge conservation is maintained. Option C) Positron emission is, therefore, the correct answer.
Notably, alpha decay occurs when a nucleus ejects an alpha particle and it is common in very heavy nuclei. Beta-minus decay involves a neutron transforming into a proton and emitting an electron, and gamma decay involves the emission of pure energy in the form of photons without changing the number of protons or neutrons in the nucleus.