Types of Nuclear Reactions

Why This Matters

Nuclear reactions sit at the heart of physics—they explain how stars shine, why certain elements exist, and how we harness atomic energy. In Principles of Physics III, you're being tested on your ability to distinguish between different reaction mechanisms: spontaneous decay vs. induced reactions, mass-energy equivalence, conservation laws, and binding energy changes. These concepts appear repeatedly in problems asking you to balance nuclear equations, calculate energy release, or predict reaction products.

Don't just memorize that "fission splits atoms" or "fusion combines them." Know why each reaction occurs (stability seeking, energy minimization), what conservation laws apply (baryon number, charge, lepton number), and how to calculate energy release using $\Delta E = \Delta m c^2$. When you understand the underlying physics, you can tackle any nuclear reaction problem—even ones involving isotopes you've never seen.

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Spontaneous Decay Processes

These reactions occur without external input—unstable nuclei naturally transform to reach more stable configurations. The driving force is always the nucleus seeking a lower energy state with greater binding energy per nucleon.

Radioactive Decay (Overview)

• Spontaneous nuclear transformation—unstable nuclei emit radiation to achieve stability, governed by exponential decay law $N(t) = N_0 e^{-\lambda t}$
• Transmutation occurs when the parent nucleus becomes a different element or isotope, moving toward the band of stability on the N-Z chart
• Three primary modes: alpha, beta, and gamma decay, each with distinct particles emitted and conservation rules to track

Alpha Decay

• Emission of an alpha particle ($^4_2\text{He}$)—decreases atomic number by 2 and mass number by 4, written as $^A_Z X \rightarrow ^{A-4}_{Z-2}Y + ^4_2\alpha$
• Common in heavy nuclei like $^{238}\text{U}$ and $^{226}\text{Ra}$ where the strong force can't fully overcome Coulomb repulsion
• Low penetration ability due to large mass and +2 charge; stopped by paper or skin, but highly ionizing

Beta Decay

• Weak force transformation—converts neutrons to protons ($\beta^-$) or protons to neutrons ($\beta^+$), always emitting a neutrino to conserve lepton number
• Beta-minus: $n \rightarrow p + e^- + \bar{\nu}_e$, increases atomic number by 1; occurs in neutron-rich nuclei
• Beta-plus: $p \rightarrow n + e^+ + \nu_e$, decreases atomic number by 1; occurs in proton-rich nuclei

Gamma Decay

• High-energy photon emission—nucleus transitions from excited state to ground state without changing composition: $^A_Z X^* \rightarrow ^A_Z X + \gamma$
• No change in atomic or mass number—same element, just lower energy state
• Often follows alpha or beta decay when the daughter nucleus forms in an excited configuration

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Particle Emission Reactions

Beyond the "big three" decay modes, nuclei can emit individual nucleons under specific conditions. These processes are rarer but crucial for understanding nuclear chain reactions and exotic isotopes.

Neutron Emission

• Direct ejection of neutrons—occurs in highly excited nuclei or as products of fission reactions
• Critical for chain reactions: emitted neutrons can induce fission in nearby $^{235}\text{U}$ nuclei, enabling sustained reactions in reactors
• No charge change—atomic number stays constant, but mass number decreases by 1 per neutron emitted

Proton Emission

• Rare decay mode—observed only in extremely proton-rich isotopes beyond the proton drip line
• Decreases atomic number by 1 and mass number by 1: $^A_Z X \rightarrow ^{A-1}_{Z-1}Y + p$
• Requires overcoming Coulomb barrier—proton must tunnel out, making this process much less common than alpha decay

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Electron-Related Transformations

These processes involve the nucleus interacting with electrons or their antiparticles. Both achieve the same nuclear result—converting a proton to a neutron—but through different mechanisms.

Electron Capture

• Inner electron absorbed by nucleus—combines with a proton to form a neutron: $p + e^- \rightarrow n + \nu_e$
• Decreases atomic number by 1 without emitting a positron; competes with $\beta^+$ decay in proton-rich nuclei
• Characteristic X-rays emitted when outer electrons fill the vacancy left by the captured electron

Positron Emission

• Antimatter production—proton converts to neutron while emitting a positron ($e^+$) and neutrino
• Decreases atomic number by 1: $^A_Z X \rightarrow ^A_{Z-1}Y + e^+ + \nu_e$
• Medical applications: PET scans detect gamma rays from positron-electron annihilation ($e^+ + e^- \rightarrow 2\gamma$)

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Induced Nuclear Reactions

Unlike spontaneous decay, these reactions require an external trigger—typically a bombarding particle. The key physics involves overcoming the Coulomb barrier and achieving critical conditions for sustained reactions.

Nuclear Fission

• Heavy nucleus splits into lighter fragments after absorbing a neutron: $^{235}\text{U} + n \rightarrow ^{141}\text{Ba} + ^{92}\text{Kr} + 3n + \text{energy}$
• Chain reaction potential—each fission releases 2-3 neutrons that can trigger more fissions; controlled in reactors, uncontrolled in weapons
• Energy release from binding energy difference: products have higher binding energy per nucleon than parent, releasing ~200 MeV per fission

Nuclear Fusion

• Light nuclei combine to form heavier nucleus: $^2_1\text{H} + ^3_1\text{H} \rightarrow ^4_2\text{He} + n + 17.6 \text{ MeV}$
• Powers all main-sequence stars—the Sun fuses hydrogen via the proton-proton chain at core temperatures of ~15 million K
• Requires extreme conditions to overcome Coulomb repulsion between positive nuclei; plasma confinement remains the key engineering challenge

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Quick Reference Table

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Self-Check Questions

1. Which two decay processes both result in a decrease of atomic number by 1, and what distinguishes when each occurs?

2. A nucleus undergoes alpha decay followed by gamma emission. Write the general equation and explain why gamma decay often follows alpha decay.

3. Compare fission and fusion in terms of binding energy per nucleon—why do both release energy despite being opposite processes?

4. An FRQ gives you a proton-rich isotope with decay energy of 0.5 MeV. Which process will occur: electron capture or positron emission? Justify your answer using energy requirements.

5. Why can neutron emission sustain a chain reaction in $^{235}\text{U}$ while proton emission cannot? Connect your answer to the Coulomb barrier concept.