Final answer:
After emitting a β-particle, the radioactive nucleus still contains 128 nucleons, as only a high-speed electron is ejected and the mass number remains the same.
Step-by-step explanation:
When a radioactive nucleus emits a β-particle (beta particle), it undergoes a process known as beta decay. In this process, a neutron in the nucleus is converted into a proton, and a beta particle, which is a high-speed electron, is ejected. The atomic number of the element increases by one, but the mass number remains the same because the mass of an electron is negligible compared to that of a neutron or a proton. Therefore, the number of nucleons, which includes both protons and neutrons, remains unchanged.
Regarding the question, if a nucleus contains 128 nucleons and emits a β-particle, it will still contain 128 nucleons after the emission. The correct answer is C) 128.