Key Concepts in Nuclear Reactions

Why This Matters

Nuclear reactions sit at the heart of atomic physics because they reveal how energy and matter are fundamentally connected. When you study fission, fusion, and radioactive decay, you're exploring the mechanisms that power stars, fuel nuclear reactors, and explain why certain isotopes are stable while others aren't. These concepts tie directly to conservation laws, mass-energy equivalence, binding energy, and nuclear stability—all of which appear regularly on exams.

You're being tested on more than definitions here. Exam questions will ask you to predict decay products, compare energy releases between reaction types, and explain why nuclei undergo specific transformations. Don't just memorize that alpha decay emits a helium nucleus—know why heavy nuclei favor this pathway and how it changes the parent atom. Understanding the underlying physics will help you tackle FRQs that require you to analyze unfamiliar scenarios.

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Energy-Releasing Reactions: Fission and Fusion

These are the heavy hitters of nuclear physics—reactions that convert mass into enormous amounts of energy according to $E = mc^2$. The key principle is binding energy per nucleon: nuclei move toward configurations with greater binding energy, releasing the difference as kinetic energy and radiation.

Nuclear Fission

• Heavy nucleus splits into lighter fragments—typically producing two mid-mass nuclei, several neutrons, and roughly 200 MeV of energy per event
• Chain reactions occur when released neutrons trigger additional fission events in nearby fissile material like $^{235}\text{U}$ or $^{239}\text{Pu}$
• Binding energy curve explains why fission releases energy: products have higher binding energy per nucleon than the heavy parent nucleus

Induced Fission

• Neutron absorption initiates the split—a thermal (slow) neutron is captured by a fissile nucleus, making it unstable enough to fragment
• Critical mass determines whether a chain reaction sustains itself, grows, or dies out
• Reactor control relies on moderators to slow neutrons and control rods to absorb excess neutrons, regulating the reaction rate

Spontaneous Fission

• No external trigger required—very heavy nuclei like $^{252}\text{Cf}$ can split on their own due to quantum tunneling through the fission barrier
• Competes with alpha decay in transuranic elements, with spontaneous fission becoming more probable as atomic number increases
• Neutron source applications—californium-252's spontaneous fission makes it useful for neutron radiography and starting nuclear reactors

Nuclear Fusion

• Light nuclei combine to form heavier products—the sun fuses hydrogen into helium through the proton-proton chain, releasing about 26 MeV per helium nucleus formed
• Coulomb barrier must be overcome for nuclei to get close enough for the strong force to bind them, requiring temperatures of millions of kelvin
• Binding energy curve shows why fusion of light elements releases energy: the products have higher binding energy per nucleon than the reactants

Thermonuclear Reactions

• Extreme temperatures drive fusion—"thermonuclear" specifically refers to fusion powered by thermal kinetic energy, as in stellar cores and hydrogen bombs
• Deuterium-tritium fusion ($^{2}\text{H} + ^{3}\text{H} \rightarrow ^{4}\text{He} + n$) is the most accessible reaction for controlled fusion, requiring "only" about 100 million kelvin
• Energy density far exceeds fission—fusion fuel contains roughly four times more energy per unit mass than fission fuel

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Radioactive Decay: Particle Emission

Unstable nuclei achieve stability by emitting particles. The type of decay depends on whether the nucleus has too many protons, too many neutrons, or simply too much mass.

Alpha Decay

• Emits a helium-4 nucleus ($^{4}_{2}\text{He}$)—the daughter nucleus has mass number reduced by 4 and atomic number reduced by 2
• Favored by heavy nuclei ($Z > 82$) because the alpha particle is exceptionally stable with high binding energy
• Quantum tunneling allows the alpha particle to escape despite being classically trapped by the nuclear potential well

Beta-Minus Decay ($\beta^-$)

• Neutron converts to proton—emits an electron and antineutrino, increasing atomic number by 1 while mass number stays constant
• Occurs in neutron-rich nuclei that lie above the band of stability on the chart of nuclides
• Continuous energy spectrum of emitted electrons led to the neutrino's discovery (to conserve energy and momentum)

Beta-Plus Decay ($\beta^+$)

• Proton converts to neutron—emits a positron and neutrino, decreasing atomic number by 1 while mass number stays constant
• Occurs in proton-rich nuclei that lie below the band of stability
• Requires mass difference of at least $2m_e c^2$ (1.022 MeV) between parent and daughter to be energetically possible

Positron Emission

• Identical outcome to $\beta^+$ decay—a proton becomes a neutron, releasing a positron ($e^+$) and neutrino
• PET scans use positron-emitting isotopes; the positron annihilates with an electron, producing two 511 keV gamma rays traveling in opposite directions
• Competes with electron capture in proton-rich nuclei, with the branching ratio depending on decay energy and atomic number

Neutron Emission

• Direct ejection of a neutron—occurs in extremely neutron-rich nuclei, often immediately following beta decay (delayed neutron emission)
• Mass number decreases by 1 while atomic number remains unchanged, producing a different isotope of the same element
• Critical for reactor control—delayed neutrons from fission products give operators time to adjust control rods

Proton Emission

• Direct ejection of a proton—a rare decay mode occurring in extremely proton-rich nuclei beyond the proton drip line
• Atomic number decreases by 1 and mass number decreases by 1, transforming the element
• Quantum tunneling through the Coulomb barrier enables escape, similar to alpha decay but less probable due to lower binding energy of a single proton

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Radioactive Decay: Energy and Electron Transitions

Some decay processes don't emit massive particles from the nucleus itself but instead involve energy release or interaction with atomic electrons.

Gamma Emission

• High-energy photon released—occurs when a nucleus in an excited state drops to a lower energy state, with no change in $A$ or $Z$
• Often follows other decays—after alpha or beta decay, the daughter nucleus may be left in an excited state and de-excites via gamma emission
• Discrete energies of gamma rays reveal nuclear energy level structure, analogous to atomic emission spectra

Electron Capture

• Inner-shell electron absorbed by nucleus—combines with a proton to form a neutron, decreasing atomic number by 1
• Competes with $\beta^+$ decay in proton-rich nuclei, but electron capture has no energy threshold since no positron mass is created
• Characteristic X-rays are emitted when outer electrons fill the vacancy left by the captured electron

Nuclear Isomerism

• Metastable excited states—isomers are nuclei with the same $A$ and $Z$ but different energy states, often with measurably long half-lives
• Isomeric transitions release gamma rays when the nucleus finally de-excites to its ground state
• Medical applications—technetium-99m (the "m" denotes metastable) is widely used in diagnostic imaging due to its 6-hour half-life and clean gamma emission

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Nuclear Transformations: Changing Elements

These processes convert one element into another through particle interactions, whether occurring naturally or induced in laboratories.

Nuclear Transmutation

• Element conversion via nuclear reaction—can occur through decay, particle bombardment, or neutron capture, changing the identity of the atom
• Artificial transmutation was first achieved by Rutherford in 1919, bombarding nitrogen with alpha particles to produce oxygen
• Transuranium elements ($Z > 92$) are all produced artificially through transmutation reactions in reactors or accelerators

Neutron Capture

• Nucleus absorbs a neutron—forms a heavier isotope of the same element, which may be stable or undergo subsequent decay
• S-process and r-process in stars build heavy elements through slow and rapid neutron capture, respectively
• Activation analysis—bombarding samples with neutrons creates radioactive isotopes whose gamma emissions identify trace elements

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Quick Reference Table

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Self-Check Questions

1. Which two decay processes both decrease the atomic number by 1 but differ in whether a particle is emitted from the nucleus or an electron is absorbed? How would you distinguish between them experimentally?

2. A nucleus lies below the band of stability (proton-rich). List three possible decay modes it might undergo, and explain what determines which one dominates.

3. Compare and contrast fission and fusion in terms of: (a) which part of the binding energy curve each exploits, (b) the conditions required to initiate each, and (c) current technological applications.

4. An FRQ presents an unknown radioactive source. The decay produces no change in mass number or atomic number. What type of emission is occurring, and what does this tell you about the nucleus before and after the decay?

5. Explain why alpha decay is common in heavy elements but proton emission is rare, even though both reduce the atomic number. Reference binding energy and tunneling probability in your answer.