(a) Which of the following are required characteristics of an isotope to be used as a fuel in a nuclear power reactor? (i) It must emit gamma radiation. (ii) On decay, it must release two or more neutrons. (iii) It must have a half-life less than one hour. (iv) It must undergo fission upon the absorption of a neutron. (b) What is the most common fissionable isotope in a commercial nuclear power reactor?

An isotope is an atom with the same number of protons, but a different number of neutrons. For an isotope to be used as a fuel in a nuclear power reactor, it must undergo nuclear fission (splitting of atomic nuclei), release enough energy for a sustained chain reaction, and be able to be controlled and moderated.

(i) Emitting gamma radiation is not a required characteristic for an isotope to be used as nuclear fuel. Gamma radiation is a byproduct of nuclear fission, but it does not directly contribute to the fission process. (ii) An isotope that releases two or more neutrons when it decays, can help sustain a chain reaction. This is a required characteristic for nuclear fuel. (iii) Having a half-life less than one hour is not a required characteristic for nuclear fuel. A short half-life could be problematic as the isotopes may decay too quickly, requiring frequent replacement and making the fuel less practical for use in a reactor. (iv) The ability to undergo fission upon neutron absorption is a required characteristic for nuclear fuel, as it is the primary process that generates energy in a nuclear reactor. In summary, of the given conditions, (ii) and (iv) are required characteristics of an isotope to be used as a fuel in a nuclear power reactor.

The most common fissionable isotope used in commercial nuclear power reactors is Uranium-235 (\(^{235}\)U). This isotope undergoes fission upon absorbing neutrons, releasing energy and more neutrons to sustain a chain reaction, making it suitable for use as nuclear fuel.