Nuclear Energy Comprehensive Study Guide

The Atomic Nucleus and Isotopic Variations

• Composition of the Nucleus: The nucleus of an atom contains two primary subatomic particles: protons and neutrons.

  • Protons: Positively charged particles ($+$).

  • Neutrons: Particles with no net charge (neutral).

  • Mass Comparison: The masses of protons and neutrons are very similar.

• Defining Atomic Metrics:

  • Atomic Number ($Z$): This corresponds to the number of the element on the periodic table and represents the exact number of protons in the nucleus.

  • Mass Number ($A$): The sum of the number of protons and the number of neutrons ($A = \text{protons} + \text{neutrons}$).

  • Note: The mass number is not found on the periodic table because it varies depending on the specific isotope of the element.

• Isotopes: These are versions of the same element that have the same number of protons but differ in the number of neutrons, resulting in different mass numbers.

• Nuclear Notation: Isotopes are represented using the symbol ${^A_Z}X$, where $A$ is the mass number, $Z$ is the atomic number, and $X$ is the chemical symbol.

  • Example (Carbon Isotopes): Carbon always has 6 protons. Carbon-12 (${^{12}_{\text{ }6}}\text{C}$) has 6 neutrons; Carbon-13 (${^{13}_{\text{ }6}}\text{C}$) has 7 neutrons; Carbon-14 (${^{14}_{\text{ }6}}\text{C}$) has 8 neutrons.

Nuclear Stability and Radioactive Decay

• Force Interactions:

  • Electrostatic Repulsion: Protons carry like positive charges and naturally repel each other.

  • Strong Nuclear Force: This force acts to keep the nucleus bound together, overcoming the electromagnetic repulsion between protons.

  • Role of Neutrons: Neutrons help disperse the repulsive forces of the protons and provide additional support for the strong nuclear force.

• Radioactive Decay: When a nucleus is unstable—meaning the repulsive forces between protons are stronger than the strong nuclear force—it will undergo radioactive decay to achieve a more stable state.

Types of Nuclear Radiation and Decay Processes

• Alpha ($\alpha$) Decay:

  • Alpha Particle: Consists of 2 protons and 2 neutrons. Because it has 2 protons, it is essentially a Helium nucleus, represented as ${^4_2}\text{He}$ or $\alpha$.

  • Process Change: The mass number ($A$) decreases by 4, and the atomic number ($Z$) decreases by 2.

  • Example: Radium-226 (${^{226}_{\text{ }88}}\text{Ra}$) undergoes alpha decay to produce Radon-222 (${^{222}_{\text{ }86}}\text{Rn}$) and an alpha particle.

• Beta ($\beta$) Decay:

  • Beta Particle: A high-energy electron (${^0_{-1}}\text{e}$) emitted from the nucleus.

  • Mechanism: A neutron transforms into a proton and an electron. The electron is ejected while the proton stays in the nucleus, creating a more stable proton-to-neutron ratio.

  • Governing Force: Governed by the weak nuclear force.

  • Process Change: The mass number ($A$) remains unchanged, while the atomic number ($Z$) increases by 1.

  • Example: Strontium-90 (${^{90}_{38}}\text{Sr}$) undergoes beta decay to produce Yttrium-90 (${^{90}_{39}}\text{Y}$) and a beta particle.

  • Note: There are two types (positive and negative beta decay); negative decay involves electron emission, while positive involves positron emission. Science 30 focuses primarily on negative decay ($\beta^-$).

• Gamma ($\gamma$) Decay:

  • Gamma Photons: High-energy electromagnetic radiation (photons).

  • Mechanism: Often follows alpha or beta decay when a nucleus is in an excited state ($X^*$). The emission of gamma photons lowers the atoms' energy state without changing the number of protons or neutrons.

  • Process Change: Mass number ($A$) and atomic number ($Z$) both remain unchanged.

  • Example: Barium-137 (${^{137}_{\text{ }56}}\text{Ba}^*$) emits a gamma photon ({^0_0}\text{\gamma}) to become stable Barium-137 (${^{137}_{\text{ }56}}\text{Ba}$).

Decay Comparison and Equations

Properties and Shielding of Radiation

• Ionization and Penetration:

  • Alpha ($\alpha$): High ionization ability but very low penetration. It can be stopped by a single sheet of paper.

  • Beta ($\beta$): Moderate ionization and moderate penetration. It can pass through paper but is stopped by a thin sheet of aluminum.

  • Gamma ($\gamma$): Low ionization ability but very high penetration. It requires thick lead or several meters of concrete to be shielded effectively.

• Detection: Geiger counters are used to measure the amount of radiation present and test the effectiveness of different shielding materials.

Practical Applications of Radiation

• Alpha Radiation Uses:

  • Smoke Detectors: Contain Americium-241 (${^{241}}\text{Am}$), which ionizes air to detect smoke particles.

  • Power Sources: Used to power heart pacemakers and space probes, such as the Mars Curiosity Rover.

• Beta Radiation Uses:

  • Medicine: Used as tracers for internal body imaging and in cancer treatments.

  • Industry: Used to locate leaks in underground pipes and to gauge the thickness of industrial materials during production.

• Gamma Radiation Uses:

  • Sterilization: Used to sterilize medical equipment and packaged foods.

  • Astronomy: Gamma ray detection is used by telescopes to create images of the universe.

  • Medicine: Used in targeted cancer treatments to kill malignant cells.

Nuclear Fission and Power Generation

• Fission Process: The splitting of a large, heavy nucleus into smaller, lighter nuclei, releasing a significant amount of energy.

  • Initiation: A neutron bombards a large atom (e.g., Uranium-235), creating an unstable isotope (Uranium-236) that splits.

  • Chain Reaction: The splitting process releases additional neutrons, which then bombard other nearby atoms, causing a self-sustaining chain reaction.

• Anatomy of a Nuclear Reactor:

  1. Containment Structure: Encloses the reactor to prevent radiation leaks.

  2. Nuclear Reactor Core: Where fission occurs.

  3. Fuel Rods: Contain Uranium oxide pellets.

  4. Control Rods: Made of Boron or Cadmium; they are lowered into the reactor to absorb neutrons and slow the reaction, or raised to increase it.

  5. Moderator: Usually water or graphite; slows down neutrons so they can be absorbed by Uranium atoms to maintain the reaction.

  6. Coolant: Usually water; absorbs the heat from the fission reaction.

  7. Heat Exchange: Heat turns water into steam.

  8. Turbine: High-pressure steam drives the turbine.

  9. Generator: The spinning turbine drives a generator to produce electricity.

  10. Condenser/Cooling Towers: Steam is cooled back into water to be recycled.

Nuclear Waste and Environmental Concerns

• Spent Fuel Composition:

  • Uranium-238: $95\%$

  • Fission Products: $3\%$

  • Plutonium: $1\%$

  • Uranium-235: $1\%$

• Classification of Waste:

  • Low Level Waste (LLW): $90\%$ of volume, $1\%$ of radioactivity. Includes items like tools or clothing. Activity limits: $< 4 \text{GBq/t}$ for alpha, $< 12 \text{GBq/t}$ for beta-gamma.

  • Intermediate Level Waste (ILW): $7\%$ of volume, $4\%$ of radioactivity. Includes metal fuel cladding.

  • High Level Waste (HLW): $3\%$ of volume, but $95\%$ of total radioactivity. Produces heat ($> 2 \text{kW/m}^3$) and requires dedicated cooling and shielding.

• Disposal Methods:

  • Near-Surface: For LLW; compacted into steel canisters and stored in concrete vaults.

  • Deep Geological Disposal: For ILW and HLW; stored $250\,\text{m}$ to $1000\,\text{m}$ underground in stable rock formations. HLW is often incorporated into glass (vitrification) and stored for 50 years to cool before permanent disposal.

• Safety Concerns:

  • Meltdowns: Failure of safety measures (e.g., Chernobyl, Three Mile Island, Fukushima) can lead to devastating environmental impacts carried by wind and water.

  • Security: Risks of radioactive materials being stolen for weapons.

  • Waste Longevity: Isotopes like Pu-239 have half-lives of up to $24,000$ years; some waste (I-129) lasts up to $16,000,000$ years.

Nuclear Fusion

• Fusion Process: The opposite of fission; smaller atoms collide and fuse to create larger atoms.

• Occurrence: Fusion is the process that powers stars.

• Example Reaction: Two atoms of heavy hydrogen ($H-2$, or Deuterium) collide to create Helium-3 (${^3_2}\text{He}$).

Mass-Energy Equivalence

• Concept: Albert Einstein demonstrated that mass and energy are interchangeable. In nuclear reactions, any loss of mass between reactants and products is converted into energy.

• Formula: $E = mc^2$

  • $E$ = Energy in Joules ($\text{J}$)

  • $m$ = Mass in kilograms ($\text{kg}$)

  • $c$ = Speed of light ($3.00 \times 10^8 \text{m/s}$)

Nuclide Mass Data Reference (Table Values in $10^{-3} \text{kg/mol}$)

• Barium-141 (${^{141}}\text{Ba}$): $140.91441$

• Beryllium-7 (${^7}\text{Be}$): $7.01693$

• Beryllium-8 (${^8}\text{Be}$): $8.00531$

• Boron-8 (${^8}\text{B}$): $8.02461$

• Carbon-14 (${^{14}}\text{C}$): $14.00324$

• Cesium-144 (${^{144}}\text{Cs}$): $143.93202$

• Fluorine-17 (${^{17}}\text{F}$): $17.00210$

• Helium-3 (${^3}\text{He}$): $3.01603$

• Hydrogen-1 (${^1}\text{H}$): $1.00783$

• Hydrogen-2 (Deuterium): $2.01410$

• Hydrogen-3 (Tritium): $3.01603$

• Krypton-92 (${^{92}}\text{Kr}$): $91.92611$

• Lanthanum-146 (${^{146}}\text{La}$): $145.92579$

• Lead-206 (${^{206}}\text{Pb}$): $205.97446$

• Lead-208 (${^{208}}\text{Pb}$): $207.97664$

• Neon-20 (${^{20}}\text{Ne}$): $19.99244$

• Nitrogen-13 (${^{13}}\text{N}$): $13.00574$

• Nitrogen-14 (${^{14}}\text{N}$): $14.00307$

• Plutonium-239 (${^{239}}\text{Pu}$): $239.05216$

• Radium-226 (${^{226}}\text{Ra}$): $226.02540$

• Uranium-235 (${^{235}}\text{U}$): $235.04392$