# Lecture 18: Nuclear Reactions and Applications ## General Chemistry II --- ## Learning Objectives By the end of this lecture, students will be able to: 1. Explain nuclear binding energy and mass defect 2. Interpret the binding energy per nucleon curve and its implications for nuclear stability 3. Distinguish between nuclear fission and nuclear fusion 4. Describe the chain reaction mechanism in nuclear fission 5. Explain the principles of nuclear reactors and nuclear weapons 6. Describe applications of radioisotopes in medicine, industry, and research --- ## Lecture Content ### I. Mass Defect and Nuclear Binding Energy The mass of a nucleus is always less than the sum of the masses of its individual protons and neutrons. This difference, called the mass defect (Delta m), represents mass that has been converted to energy to hold the nucleus together. It is calculated as Delta m = [Z * m_p + N * m_n] - m_nucleus, where m_p = 1.00728 amu and m_n = 1.00866 amu. The energy equivalent of the mass defect is given by Einstein's famous equation E = Delta m * c^2. In nuclear physics, a convenient conversion factor is 1 amu = 931.5 MeV (million electron volts). The nuclear binding energy is defined as the energy required to completely separate a nucleus into its individual protons and neutrons. A larger binding energy means a more tightly bound and therefore more stable nucleus. ### II. Binding Energy Per Nucleon The binding energy per nucleon, obtained by dividing the total binding energy by the mass number A, is the key metric for comparing the stability of different nuclei. The binding energy per nucleon curve rises sharply for the lightest nuclei (hydrogen, helium, lithium), reaches a maximum near A = 56 (iron-56 and nickel-62 are the most stable nuclei), and then gradually decreases for heavier elements. This curve has profound implications. Nuclei lighter than iron can release energy by undergoing fusion, combining to form heavier nuclei that are closer to the stability maximum. Nuclei heavier than iron can release energy by undergoing fission, splitting into lighter fragments nearer to the peak. Iron-56 sits at the "valley of stability" where no energy can be gained from either process. A graph of binding energy per nucleon (MeV/nucleon, y-axis, range 0 to 9) vs. mass number A (x-axis, range 0 to 250). The curve rises steeply from H-1 (0) through He-4 (7.1, notably high), then Li, Be, B, C. It peaks near Fe-56 (~8.8 MeV/nucleon, labeled "Most stable"). The curve then gradually decreases through heavier elements, reaching about 7.6 for U-238. An arrow on the left side points upward labeled "Fusion releases energy." An arrow on the right side points leftward labeled "Fission releases energy." He-4, C-12, O-16, and Fe-56 are specifically labeled as peaks due to their exceptional stability. ### III. Nuclear Fission In nuclear fission, a heavy nucleus splits into two or more lighter nuclei, releasing neutrons and a tremendous amount of energy. Fission is typically induced by bombarding a fissile nucleus with a neutron. For example, ^235_92 U + ^1_0 n -> ^141_56 Ba + ^92_36 Kr + 3 ^1_0 n + energy. The products vary widely; many different pairs of fission fragments are possible. On average, 2 to 3 neutrons are released per fission event, and approximately 200 MeV of energy (about 2 x 10^13 J/mol) is liberated. The neutrons released by one fission event can trigger further fission events, creating a chain reaction. Whether this chain reaction is self-sustaining depends on the mass of fissile material present. In a subcritical mass, too many neutrons escape without causing further fissions and the reaction dies out. At the critical mass, exactly one neutron per fission event triggers another fission, sustaining a controlled chain reaction. In a supercritical mass, more than one neutron per fission triggers additional fissions, leading to an exponentially growing, explosive chain reaction. The two primary fissile materials are ^235U, which constitutes only 0.7% of natural uranium, and ^239Pu, which is produced artificially in nuclear reactors. ### IV. Nuclear Reactors A nuclear reactor maintains a controlled, self-sustaining chain reaction to produce energy. The fuel consists of enriched uranium (3-5% ^235U) in the form of UO2 pellets. A moderator, typically light water (H2O), heavy water (D2O), or graphite, slows down the fast neutrons released during fission to thermal energies, which greatly increases their probability of being captured by ^235U. Control rods made of neutron-absorbing materials such as cadmium or boron regulate the reaction rate: inserting them further slows the reaction, while withdrawing them speeds it up. A coolant, often water, transfers heat from the reactor core to generate steam, which drives turbines to produce electricity. A containment structure surrounding the reactor prevents the release of radioactive materials. The safety concerns associated with nuclear power include the risk of meltdowns (as occurred at Three Mile Island, Chernobyl, and Fukushima), the challenge of long-term radioactive waste storage, and the potential for nuclear weapons proliferation. A schematic cross-section of a pressurized water nuclear reactor. The reactor core at the center contains fuel rod assemblies (UO2 pellets in zirconium alloy tubes) and control rods that can be raised or lowered. The core is submerged in water (serving as both moderator and coolant) within a heavy steel reactor vessel. A primary cooling loop carries heated water (under high pressure to prevent boiling) to a steam generator, where heat is transferred to a secondary loop. The secondary loop produces steam that drives a turbine connected to an electrical generator. A condenser cools the steam back to water. A cooling tower provides the final heat sink. Labels identify each component and the flow direction. The containment building surrounding the reactor vessel is shown as a thick concrete structure. ### V. Nuclear Fusion In nuclear fusion, two light nuclei combine to form a heavier nucleus, releasing enormous energy. Fusion is the process that powers the sun and all other stars. The deuterium-tritium reaction, ^2_1 H + ^3_1 H -> ^4_2 He + ^1_0 n + 17.6 MeV, is the most promising candidate for terrestrial fusion energy. In stars, the proton-proton chain, ^1_1 H + ^1_1 H -> ^2_1 H + ^0_(+1) e + neutrino, initiates the process. Fusion offers several advantages over fission. The fuel, hydrogen isotopes, is abundant. The primary product, helium, is not radioactive. There is no risk of meltdown and no long-lived radioactive waste. However, fusion requires extraordinarily high temperatures (10^7 to 10^8 K) to overcome the electrostatic repulsion between positively charged nuclei (the Coulomb barrier). At these temperatures, matter exists as a plasma, which must be confined either magnetically (in a tokamak) or inertially (using powerful lasers). Controlled fusion for commercial power generation remains an active area of research but has not yet been achieved on a practical scale. Uncontrolled fusion, as in a thermonuclear weapon (hydrogen bomb), uses a fission bomb to generate the extreme temperatures needed to initiate fusion. ### VI. Applications of Radioisotopes #### Medical Applications Radioisotopes play essential roles in medical diagnosis and therapy. Technetium-99m (^99m Tc), with a half-life of 6 hours, is the most widely used medical radioisotope. As a gamma emitter, it is employed in bone scans, cardiac imaging, and many other diagnostic procedures. Iodine-131, with a half-life of 8 days, is used to image and treat thyroid disorders because the thyroid gland naturally concentrates iodine. Fluorine-18, incorporated into fluorodeoxyglucose (FDG), has a half-life of 110 minutes and is the basis of PET (positron emission tomography) scanning for cancer detection. In radiation therapy, cobalt-60 provides a powerful gamma radiation source for treating cancer. Brachytherapy involves implanting radioactive seeds, such as iodine-125 for prostate cancer, directly near tumors. #### Industrial Applications Radiotracer studies use small amounts of radioisotopes to track flow patterns, detect leaks in pipelines, and measure mechanical wear. Thickness gauges use beta or gamma radiation to measure the thickness of manufactured materials such as paper and metal sheets. Gamma radiation from cobalt-60 is used to sterilize medical equipment and preserve food. #### Research Applications Radiocarbon dating with ^14C is fundamental to archaeology and geology. Isotope tracing, using radioisotopes such as ^32P, allows researchers to follow the path of specific atoms through chemical and biological reactions, such as DNA replication. Neutron activation analysis identifies the elemental composition of samples by bombarding them with neutrons and analyzing the characteristic emissions of the resulting radioactive isotopes. A diagram showing three medical applications of radioisotopes. Panel A: A PET scan setup. A patient lies in a PET scanner ring. ^18F-FDG (fluorodeoxyglucose) has been injected. Inside the body, positrons from ^18F annihilate with electrons, producing two 511 keV gamma rays traveling in opposite directions. Detectors around the ring capture these coincident gamma rays to construct an image. A sample PET brain scan image is shown. Panel B: Thyroid uptake of ^131I. An outline of a human body shows ^131I concentrating in the thyroid gland. A gamma camera detects the emitted radiation, producing an image of thyroid function. Panel C: Radiation therapy with ^60Co. A focused beam of gamma radiation targets a tumor while minimizing exposure to surrounding healthy tissue. ### VII. Biological Effects of Radiation Ionizing radiation damages biological molecules, particularly DNA, through two mechanisms. Direct damage occurs when radiation breaks chemical bonds in DNA. Indirect damage occurs when radiation ionizes water molecules to produce highly reactive free radicals (OH*), which then attack DNA. The severity of biological damage depends on the type of radiation (alpha particles cause the most damage per unit absorbed if they are inside the body), the dose and dose rate, the area of the body exposed, and the cell type (rapidly dividing cells such as bone marrow, the gastrointestinal lining, and embryonic tissue are the most sensitive). High acute doses exceeding 1 Sv produce acute radiation syndrome, with symptoms progressing from nausea to bone marrow failure and potentially death. Chronic low-dose exposure increases cancer risk over time. Radiation safety follows the ALARA principle: exposure should be kept "As Low As Reasonably Achievable." ---