8. Radioactive Decay — Modes, Energetics, and Trends

The video begins with an introduction to radioactive decay, emphasizing its significance in the field of nuclear physics. The lecturer, Michael Short, outlines the general concept of decay and introduces the idea of creating a generalized decay diagram to understand the different decay processes. He also humorously mentions his one-year-old son's artistic intervention on a previous diagram, setting a light-hearted tone for the lecture. The audience is encouraged to participate by suggesting types of radioactive decay, starting with alpha decay.

The paragraph delves into alpha decay, describing it as the process where a helium nucleus is emitted from a parent nucleus, resulting in a daughter nucleus with two fewer protons and four fewer total nucleons. The decay diagram for alpha decay is depicted as moving to the left, signifying a decrease in atomic number and energy. The lecture continues with an exploration of beta decay, highlighting the emission of an electron (or beta particle) from the nucleus and the accompanying release of an anti-neutrino.

The lecture moves on to discuss electron capture, where a nucleus captures an electron from an inner orbital, effectively neutralizing a proton and leading to a daughter nucleus with one fewer proton. Positron emission is also covered, where a positron (the anti-matter equivalent of an electron) is emitted, resulting in the same daughter nucleus as in electron capture but through a different process. The conditions necessary for positron emission are briefly touched upon, with a promise to revisit the topic later in the course.

The paragraph covers neutron emission, where a neutron is released from an unstable nucleus, leading to a daughter nucleus with one less total nucleon. This is illustrated on the decay diagram by a downward movement, indicating a decrease in mass number. Gamma decay is introduced as the emission of a photon from the nucleus, which doesn't change the nucleus's identity but rather transitions it to a lower energy state. The paragraph concludes with a discussion of the generalized decay diagram, which encompasses all the decay types discussed.

The lecture explores the probabilities associated with different decay processes, explaining that these are typically measured due to the complexity of calculating them from first principles. The importance of half-life in understanding decay processes is mentioned, with examples provided to illustrate how half-life can vary for different decay modes of the same isotope. The concept of decay hindrance is introduced, explaining that certain energy transitions are more probable than others, leading to variations in decay patterns.

The paragraph focuses on how to read decay diagrams, including understanding the parent and daughter nuclei, energy levels, and the Q value for a reaction. The calculation for the kinetic energy of an alpha particle during alpha decay is derived using conservation laws for mass, energy, and momentum. The lecture concludes with a discussion of the different decay modes of isotopes like uranium-235 and thorium-231, and the probabilities associated with each mode.

Beta decay is discussed in detail, highlighting the continuous energy spectrum observed for beta particles, which led to the hypothesis of the neutrino. The lecture touches on the conservation of energy in beta decay and the subsequent gamma transitions that often follow. The use of beta decay in dating through carbon-14 is mentioned, along with its application in medical imaging using technetium-99m and the risks associated with cobalt-60.

The paragraph introduces positron decay, explaining the energy requirements and the relationship between the Q value, mass, and kinetic energy. Positron annihilation spectroscopy (PAS) is explored as a technique to study defects in materials by analyzing the lifetime of positrons before they annihilate with electrons. The lecture concludes with a discussion of how PAS can be used to determine the size and number of vacancies and defects in materials, which is crucial for understanding radiation damage.

The final paragraph addresses the question of which type of radioactive decay is the most dangerous. It discusses the hazards of alpha, beta, and gamma decay when ingested or when external sources are involved. The paragraph also humorously recounts a hypothetical scenario where one must choose how to handle different types of radioactive 'cookies,' highlighting the different shielding and penetration capabilities of each decay type.