Nuclear Decay Processes

Generalized Decay Diagram

• Generalized unstable nucleus decays.
• Decay diagrams have axes that help interpret them.
  • Imaginary y-axis: increasing energy.
  • Imaginary x-axis: atomic number (z).

Alpha Decay

• Parent nucleus (atomic number z, mass number a) changes.
• Alpha particle emission:
  • Alpha particle: helium nucleus ($He$) with 4 nucleons and 2 protons ($_2^4He$).
  • Daughter nucleus: $(z-2)$ protons and $(a-4)$ total nucleons.
• Equation: $^{A}_{Z}X \rightarrow _{2}^{4}He + ^{A-4}_{Z-2}Y$
• On a decay diagram, alpha decay moves to the left (decreasing z and energy).

Beta Minus Decay

• Emission of an electron from the nucleus.
• Beta particle vs. electron: Beta originates from the nucleus.
• Accompanying emission of an antineutrino ($\bar{\nu}_e$) (almost no mass, no charge).
• Daughter nucleus: one more proton, same number of total nucleons.
• Equation: $^{A}<em>{Z}X \rightarrow e^{-} + \bar{\nu}</em>e + ^{A}_{Z+1}Y$
• On a decay diagram, beta decay moves to the right (increasing z).

Electron Capture

• Nucleus captures an inner orbital electron, neutralizing a proton.
• Daughter nucleus: one fewer proton, same total nucleons.
• Equation: $^{A}<em>{Z}X + e^{-} \rightarrow ^{A}</em>{Z-1}Y + \nu_e$
• On a decay diagram, electron capture moves to the left (decreasing z).

Positron Emission

• Emission of a positron (antimatter equivalent of an electron).
• Same general characteristics as an electron but with opposite charge.
• Daughter nucleus has one fewer proton with the same mass number.
• Equation: $^{A}<em>{Z}X \rightarrow e^{+} + \nu</em>e + ^{A}_{Z-1}Y$
• Positron creation/emission and electron capture can have the same ending state.
• Requires sufficient energy to create the positron.

Neutron Emission

• Unstable nuclei (e.g., helium-5) can emit a neutron.
• Daughter nucleus: same z, one fewer total nucleon.
• Equation: $^{A}<em>{Z}X \rightarrow n + ^{A-1}</em>{Z}Y$
• On a decay diagram, neutron emission goes straight down (decreasing a).
• Observed in super neutron-rich nuclei (e.g., helium-10, emits two neutrons).

Gamma Decay

• Emission of a photon (gamma ray) from the nucleus.
• The same atom/nucleus transitions to a lower energy state.
• Nucleons can occupy higher energy states, similar to electrons.
• Releases energy as a gamma ray when transitioning to lower energy states.
• Equation: $^{A}<em>{Z}X^* \rightarrow ^{A}</em>{Z}X + \gamma$
• On a decay diagram, gamma decay may be represented by a wiggly line to a stable state.