Lecture 33: Nuclear Physics and Radioactivity

The Atomic Nucleus and the Four Fundamental Forces

• Composition of the Nucleus: The atomic nucleus is located at the center of an atom and is comprised of two types of nucleons:

  • Protons: Positively charged subatomic particles.

  • Neutrons: Subatomic particles with no electric charge (neutral).

• Rutherford Gold Scattering Experiment: Conducted in the early $20\text{th}$ century, this experiment involved shooting positively charged alpha particles at a thin gold foil.

  • Observations: Most alpha particles passed through, but some experienced very large deflections when they collided with or passed near the center of the atoms.

  • Conclusions: This confirmed that the nucleus is extremely compact and possesses a positive charge.

• The Problem of Electromagnetic Repulsion: Based on the principles of electromagnetism (where like charges repel), the positively charged protons within a nucleus should repel each other, cause the nucleus to fly apart.

• The Strong Force: The stability of the nucleus is maintained by the strong force, which is the strongest of the four fundamental forces.

  • Distance Requirement: The strong force only operates over extremely small distances (on the scale of the atomic nucleus).

  • Function: It overpowers the electromagnetic repulsion between protons to hold the nucleus together.

  • Fundamental Forces Hierarchy:

    1. The Strong Force

    2. Electromagnetism

    3. The Weak Force

    4. Gravity

• Stability and Nuclear Size: The presence of neutrons helps stabilize the nucleus. However, as the number of protons increases, the physical size of the nucleus grows. If the nucleus becomes too large, it may exceed the distance over which the strong force is effective. Elements with an atomic number of $83$ (Lead) and higher are typically unstable and undergo spontaneous radioactive decay.

Discovery and Implications of Radioactivity

• Definitions:

  • Isotopes: Elements that possess the same number of protons but different numbers of neutrons. Some isotopes are stable, while others are unstable.

  • Radioactivity: The process by which an unstable atomic nucleus breaks apart and emits particles or energy because the strong force can no longer counteract electromagnetic repulsion.

• Henri Becquerel’s Discovery: In the late $19\text{th}$ century, Becquerel discovered radioactivity by accident when a uranium sample left in a drawer exposed a photographic plate.

• Nature of Emissions: Scientific experiments using electric and magnetic fields demonstrated that radioactive emissions were not x-rays or electromagnetic waves because they could be deflected, meaning they carried an electric charge.

• Historical Misconceptions: Before the dangers were understood, there was a period of enthusiasm for radioactive products, such as radium-infused water. This led to serious health issues, including cancer, as the public was unaware of the lethal nature of high-dose radiation.

• Modern Beneficial Uses:

  • Medical: Diagnosis and treatment of conditions like cancer.

  • Archaeology: Carbon dating to determine the age of fossils.

  • Industrial: Smoke detectors use a radioactive source to detect smoke.

  • Scientific: Creation of new atoms and isotopes.

Natural Radioactive Decay: Alpha Decay

• Process: An unstable atomic nucleus emits an alpha particle to achieve stability.

• Alpha Particle Composition: A helium nucleus consisting of $2$ protons and $2$ neutrons.

• Characteristics:

  • Size: Alpha particles are the largest particles emitted during radioactive decay.

  • Penetration and Shielding: Due to their large mass, they lose energy quickly upon contact with other matter. They can be blocked by a single sheet of paper.

  • Charge: Positively charged (confirmed by deflection direction in magnetic fields).

  • Conservation Laws: During alpha decay, both the total charge (atomic number) and the total number of nucleons (atomic mass number) are conserved.

• Example Reaction: Uranium-$238$ ($^{238}\text{U}$) emits an alpha particle and transmutes into Thorium-$234$ ($^{234}\text{Th}$).

  • Total nucleons: $238 \rightarrow 234 + 4$

  • Atomic number: $92 \text{ (protons in Uranium)} \rightarrow 90 \text{ (protons in Thorium)} + 2 \text{ (protons in Alpha)}$

• Visualization: A cloud chamber can visualize alpha decay (e.g., using Lead-$210$), showing trails of condensation as particles emanate from the source.

Natural Radioactive Decay: Beta Decay

• Process: A neutron within the atomic nucleus converts into a proton. In this transformation, the nucleus emits an electron (referred to as a beta particle) and a subatomic particle called an anti-neutrino.

• Characteristics:

  • Particle Nature: The beta particle is an electron, which is much smaller than an alpha particle.

  • Charge: Negatively charged (confirmed by deflection direction in magnetic fields).

  • Penetration and Shielding: Beta particles require more shielding than alpha particles, such as several millimeters of aluminum foil.

  • Conservation Laws: Total charge and the total number of nucleons are conserved.

• Example Reaction: Thorium-$234$ ($^{234}\text{Th}$) emits an electron to become Protactinium-$234$ ($^{234}\text{Pa}$).

  • Nucleons: $234 = 234$

  • Atomic number: $90 \text{ (in Thorium)} \rightarrow 91 \text{ (in Protactinium)} - 1 \text{ (the electron)}$

• Carbon Dating:

  • Living organisms maintain a constant ratio of stable Carbon-$12$ ($^{12}\text{C}$) and unstable Carbon-$14$ ($^{14}\text{C}$).

  • After death, Carbon-$14$ is no longer replenished and undergoes beta decay.

  • The half-life of Carbon-$14$ is $5,730\,\text{years}$. Measuring the remaining ratio allows scientists to calculate the age of organic samples.

Natural Radioactive Decay: Gamma Decay

• Process: Following alpha or beta decay, a nucleus may remain in an excited state. It returns to a lower energy state by emitting gamma radiation.

• Characteristics:

  • Nature: High-energy photons; a form of ionizing radiation.

  • Charge: No electric charge (unaffected by magnetic fields).

  • Speed: Travels at the speed of light ($c$).

  • Penetration and Shielding: Extremely hazardous and difficult to block. Shielding requires heavy materials like lead, concrete, or deep water.

The Principles of Half-Life

• Definition: The average time required for exactly half of a given sample of an unstable isotope to decay.

• Probabilistic Nature: Decay is a random process. While a sample follows the half-life rule on average, any individual atom's decay time is probabilistic (similar to a coin toss).

• Range of Half-Lives:

  • Longest: Xenon-$124$ has a half-life of $10^{22}\,\text{years}$ (significantly longer than the age of the universe).

  • Shortest: Hydrogen-$5$ (synthetic) has a half-life of $10^{-23}\,\text{seconds}$.

• Asymptotic Decay Example: If starting with $100\,\text{grams}$ of an isotope with a half-life of $1\,\text{day}$:

  • After $1\,\text{day}$: $50\,\text{grams}$ remain ($50\%$ decayed).

  • After $2\,\text{days}$: $25\,\text{grams}$ remain ($75\%$ decayed).

  • After $3\,\text{days}$: $12.5\,\text{grams}$ remain ($87.5\%$ decayed).

  • After $7\,\text{days}$ ($1\,\text{week}$, $7 \text{ half-lives}$): $\text{Approximately } 99.2\%$ has decayed.

  • After $14\,\text{days}$ ($2\,\text{weeks}$, $14 \text{ half-lives}$): $\text{Approximately } 99.99\%$ has decayed.

• Completion: Theoretically, the process is asymptotic and never reaches $100\%$. Determining when the absolute last atom decays is purely probabilistic.

• Hazards of Waste: Long half-lives in radioactive waste are dangerous because they require thousands of years to reach safe levels. Furthermore, a decaying isotope may result in a "daughter" isotope that is also unstable.

Radiation Units and Human Impact

• RAD (Radiation Absorbed Dose): A measure of energy absorbed by tissue.

  • $1\,\text{RAD} = 0.01\,\text{Joules/kilogram}$ of tissue.

• REM (Roentgen Equivalent Man): A unit used to quantify biological damage to humans, as different types of radiation cause different levels of harm.

  • $1\,\text{RAD}$ of alpha radiation = $10\,\text{rems}$.

  • $1\,\text{RAD}$ of beta radiation = $1\,\text{rem}$.

• Dosage Thresholds:

  • Lethal Dose: Starts at $500\,\text{rem}$ when distributed across the whole body.

  • Survivability: Localized doses of the same amount may be survivable.

Environmental and Daily Radiation Exposure

• Natural Background Radiation: Humans are constantly exposed to radiation from the air, rocks, and minerals.

  • Annual natural dose is approximately $0.3\,\text{rem}$.

• Medical Sources: CT scans and nuclear medicine. The benefits of diagnosis are weighed against the risk of exposure.

• Radon-$222$: A heavy radioactive gas that can settle in unventilated basements. It is an alpha emitter and requires mitigation to prevent inhalation hazards.

• Human-Made/Industrial Sources:

  • Historical Testing: Atmospheric nuclear testing ($1940\text{s}$ to $1960\text{s}$; banned in $1963$). Exposure from this is decreasing daily.

  • Occupational: Some jobs require wearing dosimeters to track exposure.

  • Power Production: Burning coal releases radioactive Thorium and Uranium; coal plants are a larger source of environmental radiation than nuclear power plants.

  • Accidents: Events like Chernobyl and Fukushima, as well as nuclear waste storage.

• Smoking: Cigarettes contain Polonium-$210$, an alpha emitter. For smokers, this can represent a dominant portion of their annual radiation dose.

Artificial Transmutation

• Process: Creating new elements by smashing particles together.

• Example Reaction: Helium-$4$ and Nitrogen-$14$ are transmuted into Oxygen-$17$ and Hydrogen-$1$ (a proton).

  • $^4\text{He} + ^{14}\text{N} \rightarrow ^{17}\text{O} + ^1\text{H}$

• Alchemy and Gold: While it is scientifically possible to turn lead into gold via transmutation, it is not economically feasible. The energy cost is massive, and most gold isotopes created this way are unstable and would decay into other elements.

• Superheavy Elements: Elements with atomic numbers greater than $103$ do not exist naturally. They have been synthesized in labs and have very short half-lives.

• Radiopharmacology: Artificial transmutation is used to produce medical isotopes with very short half-lives, such as Technetium-$99$, which must be generated immediately before use for diagnosis or treatment.