(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 of 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?

Verified step by step guidance

1. Step 1: Understand the role of isotopes in nuclear reactors. Isotopes used as fuel in nuclear reactors must be capable of sustaining a chain reaction. This typically involves the isotope undergoing fission when it absorbs a neutron, releasing energy and additional neutrons.
2. Step 2: Evaluate each characteristic for part (a): (i) Emitting gamma radiation is not a requirement for an isotope to be used as fuel. (ii) Releasing two or more neutrons upon decay is important for sustaining a chain reaction, as these neutrons can induce fission in other nuclei. (iii) A half-life of less than one hour is impractical for reactor fuel, as it would decay too quickly. (iv) Undergoing fission upon neutron absorption is crucial for the isotope to be used as fuel.
3. Step 3: Identify the most common fissionable isotope for part (b). In commercial nuclear power reactors, the most common fissionable isotope is Uranium-235 (\(^{235}\text{U}\)). It is capable of sustaining a chain reaction and is used in most nuclear reactors.
4. Step 4: Consider the properties of Uranium-235. \(^{235}\text{U}\) undergoes fission when it absorbs a neutron, releasing energy and additional neutrons, which can then induce fission in other \(^{235}\text{U}\) nuclei, sustaining the chain reaction.
5. Step 5: Summarize the key characteristics of a suitable isotope for nuclear fuel: It should undergo fission upon neutron absorption and release multiple neutrons to sustain a chain reaction. The most common isotope used is \(^{235}\text{U}\).