Nuclear reactions are the heart of atomic transformations. They involve changes in the nucleus, releasing energy and particles. From alpha decay to fusion, these processes shape our understanding of matter and energy at the subatomic level.

Balanced equations help us track nuclear changes. We'll explore different types of decay, the particles involved, and antimatter. We'll also dive into fission, fusion, and the concept of half-life, key to understanding radioactivity and nuclear energy.

Nuclear Reactions

Balanced nuclear equations

• Alpha decay involves an unstable atomic nucleus emitting an alpha particle (consisting of two protons and two neutrons) and transforming into a new element
  • General equation: $^{A}{Z}X \rightarrow ^{A-4}{Z-2}Y + ^{4}_{2}\alpha$
    • $X$ represents the original element
    • $Y$ represents the new element formed after alpha decay
    • $\alpha$ represents the alpha particle
  • Example: $^{238}{92}U \rightarrow ^{234}{90}Th + ^{4}_{2}\alpha$ (Uranium-238 decays into Thorium-234 and an alpha particle)
• Beta decay occurs when a neutron in an unstable atomic nucleus transforms into a proton, emitting an electron (beta particle) and an antineutrino
  • General equation: $^{A}{Z}X \rightarrow ^{A}{Z+1}Y + ^{0}_{-1}\beta^{-} + \bar{\nu}$
    • $\beta^{-}$ represents the beta particle (electron)
    • $\bar{\nu}$ represents the antineutrino
  • Example: $^{14}{6}C \rightarrow ^{14}{7}N + ^{0}_{-1}\beta^{-} + \bar{\nu}$ (Carbon-14 decays into Nitrogen-14, a beta particle, and an antineutrino)
• Gamma emission happens when an excited atomic nucleus releases energy in the form of a high-energy photon (gamma ray) to reach a more stable state
  • General equation: $^{A}{Z}X^{} \rightarrow ^{A}{Z}X + \gamma$
    • $X^{}$ represents the excited state of the nucleus
    • $\gamma$ represents the gamma ray
  • Example: $^{60}{27}Co^{} \rightarrow ^{60}{27}Co + \gamma$ (Excited Cobalt-60 releases a gamma ray to reach a more stable state)

Particles in nuclear reactions

• Protons are positively charged particles found in the nucleus of an atom
  • Denoted by the symbol $p$ or $^{1}_{1}p$
  • The number of protons in an atom's nucleus determines its atomic number and element
  • Example: Hydrogen has 1 proton, Helium has 2 protons, Lithium has 3 protons
• Neutrons are neutral particles found in the nucleus of an atom
  • Denoted by the symbol $n$ or $^{1}_{0}n$
  • The number of neutrons in an atom's nucleus affects its isotope and mass number
  • Example: Carbon-12 has 6 neutrons, Carbon-13 has 7 neutrons, Carbon-14 has 8 neutrons
• Alpha particles consist of two protons and two neutrons (essentially a helium-4 nucleus)
  • Denoted by the symbol $\alpha$ or $^{4}_{2}\alpha$
  • Emitted during alpha decay, a type of radioactive decay
  • Example: Radon-222 undergoes alpha decay, emitting an alpha particle and transforming into Polonium-218

Antimatter and nuclear processes

• Antimatter is composed of antiparticles, which have the same mass but opposite charge and quantum properties as their corresponding particles
  • Examples include positrons (antielectrons) and antiprotons
  • When matter and antimatter collide, they annihilate each other, converting their mass into pure energy according to Einstein's equation $E=mc^2$
• Annihilation occurs when a particle and its antiparticle collide, annihilating each other and converting their mass into pure energy
  • Example: a positron and an electron annihilate, producing gamma rays
  • The energy released during annihilation is given by Einstein's equation $E=mc^2$, where $m$ is the combined mass of the particle and antiparticle, and $c$ is the speed of light
• Pair production is the inverse process of annihilation, where a high-energy photon (such as a gamma ray) interacts with matter, creating a particle-antiparticle pair
  • Example: a gamma ray with sufficient energy can create an electron-positron pair when interacting with an atomic nucleus
  • The minimum energy required for pair production is equal to the combined rest mass energy of the particle and antiparticle, given by $E=2mc^2$

Nuclear Energy Processes and Decay

• Nuclear fission is the process of splitting a heavy atomic nucleus into lighter nuclei, releasing energy and often neutrons
  • This process is used in nuclear power plants and atomic bombs
  • Example: The fission of Uranium-235 when bombarded with neutrons
• Nuclear fusion is the process of combining light atomic nuclei to form heavier nuclei, releasing a large amount of energy
  • This process powers the sun and other stars
  • Example: The fusion of hydrogen nuclei to form helium in the core of stars
• Half-life is the time required for half of a given quantity of a radioactive isotope to decay
  • It is a measure of the rate of radioactive decay and is unique to each isotope
  • Used to determine the age of archaeological and geological samples
• Radioactive decay series describes the sequential decay of unstable nuclei through various intermediate nuclides until a stable nucleus is formed
  • Example: The Uranium-238 decay series, which ends with the stable isotope Lead-206
• Binding energy is the energy required to break apart a nucleus into its constituent protons and neutrons
  • It is related to the mass defect and nuclear stability
  • Explains why certain nuclear reactions release or absorb energy