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

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

1. Beta Minus (β−) decay:

   • A neutron decays into a proton while emitting a beta particle and an antineutrino.

2. Beta Positive (β+) decay:

   • A proton decays into a neutron, emitting a positron and a neutrino.

3. Electron Capture:

   • An electron is absorbed by the nucleus.

Particle Mass and Energy

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}

  • Beta positive decay represented as: A{X}^{Z} ightarrow A{Y}^{(Z-1)} + e^{+} +
    u

Electron Capture

• Mechanism:

  • An electron from an inner (K) shell is absorbed into the nucleus.

  • The electron is transmuted into a neutron and a neutrino.

  • Vacancy in electron shell is filled by an outer shell electron, emitting X-ray radiation.

• Example:

  • For Thallium-201 (Tl-201):

  • The nuclear reaction can be represented as: A{Tl}^{201} + e^{-} ightarrow A{Hg}^{201} +
    u + E

Gamma Decay and Internal Conversion

• Gamma Emission:

  • Caused by excitation of the nucleus, energy is emitted as gamma rays indicating nuclear instability.

  • Energy balance:

    • Example: For a 140 keV gamma ray, where binding energy (BE) is 21 keV, it requires 3 keV to emit the gamma ray.

• Internal Conversion:

  • An electron may be emitted instead of a gamma ray when energy is transferred to the internally bound electron.

  • The kinetic energy of the emitted electron equals the gamma-ray energy minus the binding energy.

Characteristic X-rays and Auger Electrons

• Characteristic X-ray Production:

  • Energy computed as:

  • E_{X-ray} = (-5 ext{ keV}) - (-33 ext{ keV}) = 28 ext{ keV}

• Auger Electron:

  • Energy of the Auger electron derived similarly, accounting for electron loss filling a vacancy.

  • Kinetic Energy calculated as:

  • 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.