Notes on Unstable Nuclei, Radioactive Decay, Nuclear Fission and Fusion

Page 1: Unstable Nuclei and Radioactive Decay

• Radioactive decay is a nuclear reaction in which unstable nuclei change into new nuclei, often emitting small, high-energy particles.
• The process occurs because the original nucleus is unstable; it emits particles to become a more stable nucleus, which is often a different element.
• Types of radiation (based on charge and nature):
  • Alpha radiation: emission of a helium-4 nucleus (an alpha particle).
  • Alpha particle: a He nucleus with 2 protons and 2 neutrons, charge = +2.
  • Symbolically:
    $^{4}_{2}\mathrm{He}$
  • Beta radiation: emission of a beta particle (an electron) or a positron; related to changes inside the nucleus.
  • Beta particle (β−) is an electron (e−).
  • Positron emission (β+) is a positively charged electron (e+).
  • Gamma radiation (γ) is very high energy photons with no mass and no charge.
• Nuclear equation example (alpha decay): the decay of Radium-226 to Radon-222 via alpha emission: $^{226}<em>{88}\mathrm{Ra} \rightarrow ^{222}</em>{86}\mathrm{Rn} + ^{4}_{2}\mathrm{He}$
  • This represents loss of 2 protons and 2 neutrons from Ra, forming a new element (Rn).
• Beta decay basics (two primary forms):
  • Beta minus decay (β−): a neutron turns into a proton, emitting a beta particle (electron) and an antineutrino:
    $^{A}<em>{Z}X \rightarrow ^{A}</em>{Z+1}Y + e^{-} + \bar{\nu}_e$
  • Beta plus decay / positron emission (β+): a proton turns into a neutron, emitting a positron and a neutrino:
    $^{A}<em>{Z}X \rightarrow ^{A}</em>{Z-1}Y + e^{+} + \nu_e$
• Gamma decay: an excited nucleus releases excess energy as a gamma photon without changing its mass or charge:
  $^{A}<em>{Z}X^{*} \rightarrow ^{A}</em>{Z}X + \gamma$
• Key ideas:
  • Emission of radiation reduces the nucleus’s energy and moves toward stability.
  • Different decay modes shift the atomic number (Z) and/or mass number (A) to produce a more stable nucleus.

Page 2: Radiation Types, Nuclear Reactions (Intro), and Fission/Fusion Concepts

• Beta particle and equivalent representations:
  • A beta particle is equivalent to an electron; its emission changes the neutron-to-proton ratio in the nucleus.
• Nuclear reactions (broad concepts):
  • Fusion: two light nuclei combine to form a heavier nucleus, releasing energy.
  • Fission: a heavy nucleus splits into lighter nuclei, releasing energy.
  • Both processes involve high-energy interactions and can be induced by bombardment with other particles (e.g., neutrons, protons) or by high-energy environments.
• Fission (split into smaller nuclei):
  • Produces very large amounts of energy per event.
  • Common in, and utilized for, electricity generation in nuclear power plants.
• Fusion (combine to form heavier nucleus):
  • Two light nuclei fuse to make a heavier nucleus.
  • In fusion, more mass is lost (per reaction) than in fission, which explains its high energy yield per unit mass involved.
  • The Sun releases energy through fusion, via processes like the proton–proton chain and related reactions.
• General fusion/fission distinction (conceptual):
  • Fission releases energy by splitting heavy nuclei due to the mass defect; the resulting fragments are typically more stable than the original heavy nucleus.
  • Fusion releases energy by forming a more tightly bound nucleus from lighter constituents, with a corresponding mass defect.
• Note on energy relations: energy released in nuclear processes is tied to the mass defect via Einstein’s relation $E=\Delta m\,c^2$.

Page 3: Nuclear Fission Details and Conditions for a Chain Reaction

• Fission definition (reiterated):
  • Fission is the splitting of a large radioactive nucleus into smaller nuclei, accompanied by the release of energy and typically extra neutrons.
• Neutron-induced fission and fragments:
  • A common example is fission of Uranium-235 induced by a neutron:
    $^{235}<em>{92}\mathrm{U} + ^{1}</em>{0}n \rightarrow \text{fission fragments} + \text{neutron(s)}\,.$
  • One typical fission path (example products vary):
    $^{235}<em>{92}\mathrm{U} + ^{1}</em>{0}n \rightarrow ^{141}<em>{56}\mathrm{Ba} + ^{92}</em>{36}\mathrm{Kr} + 3\,^{1}_{0}n$
  • The fission fragments are typically lighter nuclei (e.g., barium, krypton isotopes) and several neutrons are released.
• Energy release per fission:
  • Approximately $E \approx 200\ \text{MeV}$ per fission event (order of magnitude commonly cited for U-235 fission).
• Chain reaction concept:
  • A chain reaction occurs when the neutrons released by one fission event go on to induce additional fissions in nearby fissile nuclei.
  • To sustain a chain reaction, the material must have a sufficient quantity and arrangement (often referred to as a critical mass) so that emitted neutrons almost immediately collide with other fissile nuclei rather than escaping.
  • In practical systems, moderation (slowing neutrons) and neutron-absorbing materials (control rods) influence the rate and sustainability of the chain reaction.
• Practical note (from the source content):
  • The chain reaction requires a large enough quantity of fissile material (e.g., $^{235}{92}\mathrm{U}$) in close proximity so emitted neutrons can quickly encounter other $^{235}{92}\mathrm{U}$ nuclei, sustaining the reaction and generating heat.

Page 4: Fusion Energy, Comparison with Fission, and Real-World Relevance

• Fusion basics:

  • Two light nuclei fuse to form a heavier nucleus.
  • More mass is lost in fusion than in fission per reaction, leading to substantial energy release.
  • The Sun’s energy arises from fusion processes (e.g., hydrogen fusion into helium) releasing energy that powers stars.

• Example fusion reaction (deuterium–tritium fusion, common in fusion research):
  $^{2}<em>{1}\mathrm{H} + ^{3}</em>{1}\mathrm{H} \rightarrow ^{4}<em>{2}\mathrm{He} + ^{1}</em>{0}\mathrm{n} + 17.6\ \text{MeV}$

• Energy and mass considerations:

  • The energy released in fusion is tied to the mass defect $\Delta m$ in the reaction via $E = \Delta m \; c^2.$
  • In stars and theoretical fusion power systems, the goal is to achieve a net energy gain by sustaining fusion under suitable conditions (high temperature and pressure, confinement).

• Summary of practical and conceptual implications:

  • Radioactive decay and nuclear reactions underpin energy generation (fission in reactors, fusion in stars/tentative fusion power).
  • Understanding decay pathways (alpha, beta, gamma) helps predict product nuclides and radiation hazards.
  • Fission demonstrates chain reactions and the importance of critical mass, neutron economy, and control in safe energy production.
  • Fusion illustrates a potentially higher energy density and a different set of engineering challenges (confined plasma, sustaining reactions), with real-world relevance to future energy goals.

• Key formulas to remember:

  • Alpha decay: $^{226}<em>{88}\mathrm{Ra} \rightarrow ^{222}</em>{86}\mathrm{Rn} + ^{4}_{2}\mathrm{He}$
  • Beta minus decay: $^{A}<em>{Z}X \rightarrow ^{A}</em>{Z+1}Y + e^{-} + \bar{\nu}_e$
  • Beta plus decay: $^{A}<em>{Z}X \rightarrow ^{A}</em>{Z-1}Y + e^{+} + \nu_e$
  • Gamma decay: $^{A}<em>{Z}X^{*} \rightarrow ^{A}</em>{Z}X + \gamma$
  • Fission (example path): $^{235}<em>{92}\mathrm{U} + ^{1}</em>{0}n \rightarrow ^{141}<em>{56}\mathrm{Ba} + ^{92}</em>{36}\mathrm{Kr} + 3\,^{1}_{0}n$
  • Energy per fission: $E \approx 200\ \text{MeV}$
  • Fusion example (D–T): $^{2}<em>{1}\mathrm{H} + ^{3}</em>{1}\mathrm{H} \rightarrow ^{4}<em>{2}\mathrm{He} + ^{1}</em>{0}\mathrm{n} + 17.6\ \text{MeV}$
  • Mass–energy equivalence: $E = \Delta m \; c^2$