## 22.5 Nuclear Reactions Nuclear reactions are processes in which one or more nuclides are produced from a collision between two nuclei or between a nucleus and a subatomic particle. Unlike radioactive decay, which occurs spontaneously, nuclear reactions are induced by bombarding a target nucleus with an energetic particle. These reactions result in changes to the nucleus, such as fusion, fission, or transmutation, often releasing or absorbing energy. A nuclear reaction changes the identity or characteristics of an atomic nucleus by bombarding it with an energetic particle. ## Bombarding Particles Common energetic particles used for bombardment include alpha particles, gamma ray photons, neutrons, protons, and heavy ions. These particles must possess sufficient energy to overcome the Coulomb barrier and approach the positively charged target nucleus within the range of the strong nuclear force. ## General Mathematical Representation If a nucleus 'X' is bombarded by a light particle 'a', producing a nucleus 'Y' and a light particle 'b', the reaction is written as: $$a + X \rightarrow Y + b$$ In nuclear physics, this is often abbreviated as $X(a, b)Y$. ## Energy in Nuclear Reactions (Q-value) The energy released or absorbed in a nuclear reaction is represented by 'Q', which is equivalent to the difference of the rest masses of the products and reactants: $$Q = \left(m_{\text{initial}} - m_{\text{final}}\right)c^2$$ If Q is **positive**, energy is liberated and the reaction is called **exothermic**. If Q is **negative**, energy is absorbed and the reaction is called **endothermic**. ## Examples of Nuclear Reactions ### Rutherford's First Nuclear Transmutation The first artificial nuclear transmutation was performed by Ernest Rutherford in 1919, when he bombarded nitrogen nuclei with alpha particles: $${ }_2^4\mathrm{He} + { }_7^{14}\mathrm{N} \rightarrow { }_8^{17}\mathrm{O} + { }_1^1\mathrm{H} + Q$$ ### Thermal Neutron Bombardment on Nitrogen-14 A thermal neutron has energy approximately 0.025 eV, which is equal to the energy of surrounding atoms at room temperature. When nitrogen-14 is bombarded with thermal neutrons, the following reaction occurs: $${ }_0^1\mathrm{n} + { }_7^{14}\mathrm{N} \rightarrow { }_6^{14}\mathrm{C} + { }_1^1\mathrm{H} + Q$$ This reaction produces radiocarbon-14, a proton, and releases energy in the form of heat. ### Deuteron Bombardment on Manganese-55 Deuterons (${ }_1^2\mathrm{H}$) require high energy due to their positive charge to induce a reaction with manganese-55: $${ }_1^2\mathrm{H} + { }_{25}^{55}\mathrm{Mn} \rightarrow { }_{26}^{56}\mathrm{Fe} + { }_0^1\mathrm{n} + Q$$ ## Conservation Laws All nuclear reactions must adhere to the following conservation laws: 1. **Conservation of Mass-Energy**: The total energy, including rest mass energy, is conserved in all nuclear reactions. This is related to Einstein's mass-energy equivalence equation $E = \Delta m c^2$. 2. **Conservation of Momentum**: The total momentum of the system before the reaction equals the total momentum after the reaction. 3. **Conservation of Charge**: The total charge (atomic number) is conserved in all nuclear reactions. 4. **Conservation of Nucleon Number**: The total number of protons and neutrons remains constant. ## Main Types of Nuclear Reactions Due to the low binding energy per nucleon at the extremes of the nuclear mass curve, the two most significant types of nuclear reactions are Nuclear Fusion and Nuclear Fission. In nuclear fusion, light nuclei combine to form heavier nuclei, releasing enormous amounts of energy. In nuclear fission, a heavy nucleus splits into two smaller nuclei, also releasing significant energy. Both processes are fundamental to understanding nuclear energy.