Consider the fission reaction \({ }_{0}^{1} \mathrm{n}+{ }_{92}^{235} \mathrm{U} \rightarrow{ }_{37}^{89} \mathrm{Rb}+3{ }_{-1}^{0} \mathrm{e}+3{ }_{0}^{1} \mathrm{n}+?\) (a) What is the missing fission product represented by the question mark? (b) What is it about this reaction that allows for a chain reaction? (c) How much energy, in kilojoules, is released per gram of \({ }^{235} \mathrm{U} ?\) [Molar masses: \({ }^{235} \mathrm{U}, 235.0439 \mathrm{~g} / \mathrm{mol}\) \({ }^{89} \mathrm{Rb}, 88.8913 \mathrm{~g} / \mathrm{mol} ;\) missing product, \(143.8817 \mathrm{~g} / \mathrm{mol} ;{ }_{0}^{1} \mathrm{n}, 1.00870 \mathrm{~g} / \mathrm{mol} ;\) \(\left.{ }_{-1}^{0} \mathrm{e}, 0.00055 \mathrm{~g} / \mathrm{mol}\right]\) (d) How many kilograms of TNT must be detonated to produce the same amount of energy if the energy released per gram of TNT detonated is \(2.76 \mathrm{~kJ}\) ?

Understanding the mechanism of chain reactions is essential in the study of nuclear fission reactions. A chain reaction occurs when a single process, such as the splitting of an atom, causes an effect that allows the process to continue, replicate, or expand. In the context of nuclear fission, this is most notably demonstrated when a neutron hits a heavy nucleus like uranium-235, causing it to split (fission) and release more neutrons.

These released neutrons, in turn, may interact with other uranium nuclei, leading to a self-sustaining nuclear reaction if conditions are right. For a sustainable chain reaction, there must be a critical mass of the fissile material so that neutrons can successfully encounter more fuel before escaping the material or being absorbed in non-productive reactions.

Key Requirement for Chain Reactions

In the given exercise, the nuclear fission of uranium-235 produces three neutrons for every neutron that is consumed in the reaction. This surplus of neutrons is what can potentially sustain a chain reaction. However, this is a simplified view, as in reality, conditions such as the purity and shape of the uranium, along with adequate moderation of neutron energy, play a crucial role in sustaining a chain reaction.

Nuclear reaction calculations involve the precise accounting of mass and energy according to the principles of nuclear physics. Such calculations are based on the principle of conservation of mass-energy and the laws of nuclear chemistry. When solving a nuclear reaction calculation like the one provided in the exercise, students must consider conservation of nucleon number (protons plus neutrons) and charge.

Calculating Mass Defect and Energy Release

These calculations often involve finding the 'mass defect'—the difference in mass between the reactants and products—which is correlated to the energy released in the reaction by Einstein’s famous equation, E=mc². In the given fission reaction, the mass of the reactants must equal the total mass of the products, including the missing fission product. Upon determining the mass of each reactant and product through their molar masses, one can calculate the total energy released in the reaction.

A clear and consistent use of units is crucial for these calculations. If the molar masses are given in grams per mole, as they are in the exercise, the calculated energy should be converted to appropriate units such as joules or kilojoules per gram to make sense in a physical context.

Nuclear chemistry is the sub-discipline of chemistry that deals with radioactivity, nuclear processes, and the changes in the atomic nucleus. It encompasses the study of various types of nuclear reactions, including fission, the process by which a large nucleus splits into smaller nuclei with the release of energy.

Nuclear chemistry plays a pivotal role in energy production from nuclear power plants and has applications in medical diagnostics and treatment, such as in radiation therapy for cancer patients. It also involves the study of the behavior of radioactive elements and the use of radioactive tracers in biochemical laboratories.

Radiation and Radioisotopes

Understanding the principles of radioactivity, learning how to manage radioactive materials safely, and knowing the mechanisms behind the controlled release of nuclear energy are all vital components of nuclear chemistry. Radioisotopes, which are isotopes that exhibit radioactivity, are frequently used to date materials, trace chemical pathways, and provide research insights into molecular processes.