A brief summary of the discovery of forms of ionizing radiation up to the 1932 discovery of the neutron. We introduce mass-energy equivalence for the first time and explain how these cutting-edge experiments (for their time) conclusively proved the existence of high-energy, ionizing radiation.
A survey of the different types of technologies which use ionizing radiation, including for energy, medicine, safety, resource exploration, and diagnostics. We briefly preview the physical principles behind each one, setting the stage for the next three months of detailed fundamentals.
Today we formally introduce the concept that mass is energy, by exploring trends in nuclear stability. We introduce the notation we’ll use to describe nuclei and their reactions throughout the rest of the course, and introduce nuclear binding energy, analogous to chemical binding energy. We also introduce cross sections, or per-particle nuclear reaction probabilities, showing how a simple, first-order differential equation can result in their definition.
We formally define the binding energy of a nucleus and check our definition with examples from the KAERI Table of Nuclides. We imagine that a nucleus is akin to a droplet of liquid, and construct a semi-empirical mass formula to predict its stability given any number of protons and neutrons. We then construct mass parabolas to explore which nucleus is most stable given a certain number of protons or neutrons. This helps us understand mathematically why certain isotopes undergo which types of radioactive decay, and why certain isotopes are stable.
We continue constructing example mass parabolas to explore nuclear stability, and define some of the ways in which nuclei can decay to become more stable. The concept of half-life is introduced—the time which it takes for half of an amount of one isotope to decay. We also explore superheavy elements, predicted to exist beyond those which we know by their increasing half-lives with increasing mass.
We introduce the Q-equation, which describes any reaction between any two particles which releases or absorbs energy via any nuclear process. All two-body nuclear reactions will then derive from this as simplifications. We drill how the change in mass is the change in energy, given by ‘Q,’ the amount of mass-energy converted.
One simplified Q-equation is given in elastic neutron scattering, a Q = 0 reaction where one particle simply bounces off the other. We derive the relation between the energies of the incoming and outgoing neutron energies, and use this to explain what makes a good moderator (slowing-down material) for nuclear reactors. Here we link the energy dependence of cross sections with our Q-equation result to begin designing which materials should be used to construct a nuclear reactor.
Today we formally define the various modes of radioactive decay and confirm their energetics with the Table of Nuclides. We also construct decay diagrams from scratch to aid in interpreting those on the Table of Nuclides for quick reference. Notable reactions, such as alpha decay powering smoke detectors and beta decay resulting from carbon-14, are introduced.
Lecture/recording missing
Some of the trickier aspects of radioactive decay and subsequent electronic transitions are introduced, such as characteristic x-ray emission, Auger electron emission, and competing modes of radioactive decay. The ability to perform elemental identification and mapping using these electronic transitions is described.
A formalism is derived to describe how one radioactive isotope can become another, then another, and so on. We develop first-order, linear differential equations to describe the rates of these simultaneous decay processes, and introduce a few methods of solving them—analytically (the hard way), graphically (the intuitive way, without any math), and using approximations in cases where one decay constant is wildly different than the others. We also go beyond the textbook to introduce “burning” of isotopes, or creation/destruction via nuclear reactions, and show that it can be perfectly modeled using the same equations. Production of medical isotopes and radioisotope thermoelectric generators (RTGs) are modeled using these equations.
A few example problems are posed and solved together as a class, to illustrate the theoretical topics presented in the last few lectures. Cross sections are reintroduced and incorporated into nuclear reaction rates, so they can be plugged into the series radioactive decay equations.
The concepts of solid angle (the 3D equivalent of angle) and counting rates/uncertainties are briefly introduced, before heading into the MIT Nuclear Reactor Lab to see a gamma spectrometer, and the capsule insertion/removal system to neutronically activate specimens in the reactor. Students bring in pieces of whatever they’d like to learn what is isotopically contained within.
The various ways in which high-energy photons interact with matter are introduced—photoelectric effect, Compton scattering, pair production, and nuclear reactions. Energetics of each are discussed so one can read a gamma spectrum like we saw in the NRL lab last week. We also explain how the gamma spectrometer detector works. The ashes of 1000 bananas are counted and interpreted. Prof. Short irradiates his cell phone to demonstrate “digital snow” noise in the camera’s detector.
More details of photon interactions are revealed, and a couple of mistakes from the previous day are corrected. The Klein-Nishina cross section is introduced to explain the angle-energy dependence of Compton scattering. A “from-scratch” gamma counting spectrum is created from the individual photon interactions.
Prof. Short goes to Russia, and Ka-Yen (one of the teaching assistants) explains in detail how nuclear reactors work. Concepts from the course thus far are blended with previews of future courses to physically explain how current and future nuclear reactors produce heat and energy. Aspects of safety are discussed between different designs, and the details of major reactor accidents are explained.
After a brief review of photon interactions to prepare for the problem set, the ways in which ions (charged particles) interact with nuclei are introduced. The formula for stopping power (energy loss per distance traveled through matter) is derived from a physical model, and compared with the full stopping power formula. The two are strikingly similar. Integrating the inverse of stopping power also gives the range of ions in matter—unlike photons, ions stop at nearly fixed distances in matter.
Finer points of the stopping power formula and the range of its validity are shown. Bremsstrahlung, or braking radiation, occurs when charged particles change direction. Energy loss mechanisms and their relative strengths are defined in simple ratios. The upper and lower ranges of validity for the stopping power formula are shown. Cyclotrons and synchrotrons, accelerators which make use of charged particle beams, are explained. The EDS (elemental dispersive x-ray spectroscopy) spectra from electron microscopes are also explained, for how to use charged particle beams to identify elements.
The uses of photons and ions to probe and understand matter are shown as practical examples of what we’ve learned in the past couple of weeks: electron microscopy, positron annihilation spectroscopy, elemental identification, and surface analysis via Auger electron spectroscopy. Prof. Short illustrates some techniques with examples from his PhD and undergraduate research projects.
Ka-Yen’s lecture on how nuclear reactors work is expanded upon, to spend more time on advanced fission and fusion reactors. Lots of topics related to reactor operation are conceptually introduced—moderation, absorption, leakage, fast vs. thermal spectrum, breeding fuel, neutron poisons, and temperature/density feedback. This sets the stage for student control of the MIT reactor to come shortly.
The full, seven-dimensional neutron transport equation is developed from physical intuition, and putting that intuition into math. Aspects of neutron creation and transport are introduced as needed—neutron energy birth spectrum, flux, current, and many different types of neutron cross sections (fission, capture, scattering, total). It all comes down to balance—we equate the ways in which a control volume (like a reactor) can gain and lose neutrons of a certain energy, in a certain direction.
As many simplifications as possible are made to the neutron transport equation to make it solvable. The board is turned into a rainbow mess of term-specific cancellations and simplifications to reduce the neutron transport equation into something that is almost analytically solvable by any undergraduate of math, physics, or engineering. Finally, the divergence theorem is used to transform an ugly surface integral into a simpler volume integral by introducing a diffusion relation. This makes the whole thing a linear, second-order differential equation.
The hideous neutron transport equation has been reduced to a simple one-liner neutron diffusion equation. Everyone breathes a sigh of relief as it is shown to be very solvable, and a criticality relation (a balance between neutrons created and destroyed) links the geometry of a reactor to its material of construction. Different geometrical examples (slab, cube, cylinder, sphere) of reactors are introduced as real examples of designing a nuclear reactor to support a fission chain reaction.
The students explore their data from controlling the MIT nuclear reactor. Perturbations to the criticality relations are shown, by asking hypothetical questions about changing the reactor conditions (boiling the coolant, dropping metal into the core, raising its temperature). The reactor period and point kinetics relations are introduced, which describe how fast neutrons create more neutrons, and how delayed neutrons are the key to longer-term reactor stability.
Students’ questions on the past month of material are taken and explained using more practical problem set questions. A numerical example of determining reactor criticality is shown using the AP-1000, and asking a simple question—“Will It Blend?” In other words, we take the full, real specification sheet for the AP-1000, homogenize it (perfectly mix all materials into one uniform blob), and use criticality relations to determine if it would still work. Numerical integration using Microsoft Excel is shown as a way to take real cross section data from the OECD JANIS database and plug it into our analytical formulae to solve the problem.
Using all the information from the course thus far, we explain how the Chernobyl accident happened from a technical point of view (and briefly explain the failings of Soviet culture which led to the cascading human errors). The RBMK design is shown to have positive feedback coefficients, a physically dangerous situation, which along with lack of operator knowledge about long-term neutron poison transients (xenon buildup and decay) led to the 600x increase in power in four seconds, which itself led directly to the explosion, fire, and scattering of radiation around Europe.
Prof. Short uses all the concepts introduced thus far to introduce the study of nuclear materials and radiation damage – his field of study. The concept of ionizing radiation creating nuclear displacements, not just electron ionization, is introduced as the first event in radiation damage. The structural defects produced from these displacements are shown to cluster, move, and evolve, resulting in drastic changes to material properties. Key structural material properties and their formal definitions are introduced and demystified by watching a pair of Finnish scientists smash various items with a 50 ton hydraulic press.
After our discussion of the Chernobyl accident, MIT student Jake Hecla explains the accident in far more detail, and catalogs his recent trip to the Chernobyl site, the town of Pripyat, and the newly installed sarcophagus designed to contain the exploded nuclear plant. Tons of photos of Chernobyl in its current state are shown by Jake in the context of the accident.
The lecture on nuclear materials and reactor materials is continued, linking the material properties we learned by watching the Finnish hydraulic press with the defects created by radiation damage. Key measures of reactor material health are discussed, from ductility, to ductile to brittle transition temperature (DBTT), to radiation-accelerated corrosion via radiolysis and elemental segregation are shown. Prof. Short introduces a technically riskier part of his research, aimed at directly measuring the stored energy of radiation defects as a better quantifier of material damage.
Units of radiation dose to biological organisms are introduced and demystified (there are many, but they are all related). Methods of measuring dose are introduced, as well as measuring dose by different types of radiation. The difference between dose (energy absorbed per unit mass) and damage (dose times effectiveness of radiation at causing cellular defects) is specifically introduced. Ways of using ionizing radiation for medical treatment (brachytherapy, diagnostics, x-ray and proton cancer therapy) are explained from a physical point of view. Prof. Short explains how his uncle very intelligently used principles of ionizing radiation and mass attenuation to smuggle diamonds out from Apartheid South Africa.
Prof. Short introduces a new invention which uses radiation-induced color changes in binary salts to function as a real-time dosimeter for proton cancer therapy, using physics introduced in this course. Sources of background and human-made radiation, levels of public exposure, and routes of exposure are introduced, and exposures in the form of cosmic rays, terrestrial sources, medical procedures, building materials, food, radon gas, and other sources are quantified to give intuition for how much radiation is naturally present around us.
Radiation damage to organisms is explained, starting from single electron excitations all the way to DNA/cellular damage, cell division effects, organ and organism-level damage, and radiation-induced mutations. Radiolysis of water is linked between damage to cells and damage to reactor materials. The students then embark on debunking internet articles and poorly-conceived, published scientific studies about whether cell phones cause cancer (they don’t!) by identifying incorrect physics, misinterpreted data, conflicting abstracts/conclusions, biased studies, and insufficient sample sizes/statistics. One particular internet blogger is lambasted for his apparently willful manipulation of the truth to push an erroneous message.
The longer-term effects of accumulated radiation exposure are shown from the cell to the organism level. Trends in cell division rate are linked to both the various symptoms of radiation poisoning and the relative biological susceptibility of different organs. Sources of our knowledge of the effects on large and small doses of radiation are shown, paying particular attention to our lack of definitive knowledge of the effects of very low doses of radiation.
The concept of hormesis—a little bit of a bad thing can be good—is introduced and vigorously debated by the students. Tools to find peer-reviewed, primary sources of scientific knowledge are briefly introduced so the students can find high-quality sources of information for their arguments for or against hormesis. The debate somewhat unpredictably does not end in a definitive conclusion, simply because there are enough high quality studies such that one side cannot disprove the other.
The use of ionizing radiation to sterilize and preserve the freshness of food is explained using topics from the course. Beneficial effects and required doses of food irradiation are introduced, alongside some reductions in nutritional content under certain circumstances. Costs vs. benefits are shown to be quite skewed towards benefits in terms of food safety vs. slightly diminished nutritional content only in certain cases.