Week 6: Modes of Radioactive Decay
Nuclear Physics
Week 6: Modes of Radioactive Decay
Objectives
Detail various modes of radioactive decay:
Gamma emission
Internal conversion
Explain characteristic X-ray production and Auger electron emission.
Introduce key terms:
Line of nuclear stability
Modes of decay:
Alpha decay
Beta negative decay
Beta positive decay
Electron capture
Gamma emission
Internal conversion
Q-value
Chart of nuclides
Transmutation
Isobaric transition
Isomeric transition
Parent nucleus
Daughter nucleus
Radioactive decay
What is Radioactivity?
Definition:
The phenomenon of spontaneous emission of energy from an unstable or excited nucleus.
Emission includes:
Photons
Particles
Purpose of Radioactivity:
To reach a stable state.
Involvement of Electrons:
Electrons may be involved in decay; however, radioactivity is fundamentally a nuclear phenomenon.
Chemical reactions are confined to outermost orbital electrons and do not influence the radioactive properties of a nucleus.
Key Point:
A radioactive nucleus does not impact chemical behavior. The characteristics of outer shell electrons remain unchanged regardless of radioactivity.
Parent and Daughter Nuclei
Parent Nucleus:
The unstable nucleus that undergoes decay.
Daughter Nucleus:
The nucleus that is formed after the parent emits energy.
Q-value:
Defined as the transition energy or total loss of energy during the decay process.
Radioactive Decay
Definition:
The entire process of transforming a parent nucleus into a daughter nucleus.
Involves nuclear transformation and nuclear de-excitation.
Characteristics of Radioactive Decay:
Spontaneous Process:
Moments of decay cannot be exactly predicted.
Not influenced by external events.
Results in:
Transformation of one nuclear species into another.
Conversion of mass into energy (according to Einstein's equationE=mc^2²$).
Modes of Radioactive Decay
Penetrating Distances of Radiation Types
Radiation Type | Penetrating Material | Penetrating Distance |
|---|---|---|
Alpha (α) | Paper | Low |
Beta (β) | Plastic | Moderate |
Gamma (γ) and X-rays | Lead/Concrete | High |
Alpha Decay
Involves the emission of an alpha particle (helium nucleus).
Beta Decay Types:
Beta Minus (β−)
Beta Positive (β+)
Electron Capture:
The nucleus captures an electron.
Gamma Emission:
Energy is emitted in the form of gamma rays.
Line of Stability
**Nuclear Stability:
n/p ratio:**
Indicates the stability of nuclides.
Line of Stability Proposal:
Commonly represented on a chart where stable isotopes fall within the band defined by the neutron/proton ratio (n/p).
Characteristics of Stable Nuclides:
No stable nuclides exist beyond atomic number 82 (Lead).
Types of Nuclear Transitions
Isobaric Decay
Beta Minus (β−) decay:
A neutron decays into a proton while emitting a beta particle and an antineutrino.
Beta Positive (β+) decay:
A proton decays into a neutron, emitting a positron and a neutrino.
Electron Capture:
An electron is absorbed by the nucleus.
Particle Mass and Energy
Particle | Mass (atomic mass units, u) | Equivalent Energy (MeV) |
|---|---|---|
Neutron (n) | 1.008665 | 939.565 |
Proton (p) | 1.007276 | 938.272 |
Difference: | 0.001389 | 1.293 |
Beta Particle Radiation
Beta Minus Decay Example:
For Calcium-40 from Potassium-40:
Emission involves:
Antineutrino and beta particle (−1β).
Beta Positive Decay Example:
Positron Emission:
Produces two photons of 511 keV upon annihilation with an electron.
Decay expressions:
Beta negative decay represented as: A{X}^{Z} ightarrow A{Y}^{(Z+1)} + e^{-} + ar{
u} A{X}^{Z} ightarrow A{Y}^{(Z-1)} + e^{+} +
u A{Tl}^{201} + e^{-} ightarrow A{Hg}^{201} +
u + E E_{X-ray} = (-5 ext{ keV}) - (-33 ext{ keV}) = 28 ext{ keV}E_{Auger} = 28 ext{ keV} - 5 ext{ keV} = 23 ext{ keV}$$
Fluorescent Yield
Defined as the likelihood that a characteristic X-ray is emitted in place of an Auger electron.
Fluorescent Yield Rule:
Heavier elements tend to have higher fluorescent yields due to more pronounced electron interactions.
Summary of Decay Modes
Alpha Decay:
Emission of 2 protons and 2 neutrons (He nucleus).
Beta Decays:
Beta Minus (β−): Neutron to proton transition.
Beta Positive (β+): Proton to neutron transition.
Electron Capture:
Electron enters nucleus converting proton to neutron.
Gamma Emission:
Photon emitted representing energy release.
Conclusion
Mastery of modes of radioactive decay, including gamma emission, internal conversion, and understanding characteristic X-rays and Auger electron emission is essential for advanced nuclear physics study.