Nuclear Decay – Comprehensive Bullet-Point Notes

Vocabulary

• Alpha particle
  • Consists of $2$ protons and $2$ neutrons (identical to the nucleus of a $^4_2\text{He}$ atom).
  • Charge $= +2$; relatively heavy and low-penetrating.
• Beta particle
  • High-energy electron ($^0<em>{-1}\beta$) emitted when a neutron converts to a proton, or a positron ($^0</em>{+1}\beta$) emitted when a proton converts to a neutron.
  • Mass number $=0$; charge $=-1$ (electron) or $+1$ (positron).
• Gamma ray ( $\gamma$ )
  • Massless, uncharged, high-energy electromagnetic wave released from an excited nucleus.
• Isotope
  • Atoms of the same element (same atomic number $Z$) but different mass numbers $A$.
• Mass number ( $A$ )
  • Total number of protons $+$ neutrons in the nucleus.
• Atomic number ( $Z$ )
  • Number of protons; identifies the element.
• Daughter product
  • The nuclide produced after a decay event.
• Nuclear decay / Radioactivity
  • Spontaneous transformation of an unstable nucleus accompanied by emission of particles and/or energy.

Subatomic-Particle Quick Reference (Prior Knowledge Table)

• Proton: located in nucleus, charge $+1$, mass $\approx 1\,\text{u}$.
• Neutron: nucleus, charge $0$, mass $\approx 1\,\text{u}$.
• Electron: orbitals, charge $-1$, mass $\approx 0\,\text{u}$ (about $1/1836$ of a proton).
• Key relationship: $A = Z + N$ (mass number equals protons plus neutrons).
• Example: Helium-4 has $Z=2$, $N=2$, so $A=4$.

Activity A – Alpha Decay (Uranium-238)

• Observation
  • Alpha particle visibly ejects from $^{238}_{92}\text{U}$ along with a $\gamma$ ray.
• Predicted nuclear changes
  • Atomic number $Z$ decreases by $2$.
  • Mass number $A$ decreases by $4$.
• Calculated equation
  • $^{238}<em>{92}\text{U} \;\rightarrow\; ^{234}</em>{90}\text{Th} \; + \; ^4_2\text{He} \; + \; \gamma$
  • Daughter isotope: Thorium-234.
• Significance & patterns
  • Alpha decay lowers both $A$ and $Z$, moving nuclide two columns left on the periodic table.
  • Emitted $\alpha$ is relatively heavy; low penetration but high ionising power—important for smoke detectors and radon health hazards.

Activity B – Beta Decay (Carbon-14)

• Microscopic view
  • Inside the nucleus, one neutron converts into a proton + electron + antineutrino (not shown in Gizmo).
  • The electron exits as a beta particle; a gamma ray often accompanies.
• Observations
  • Neutron $\rightarrow$ proton; atomic number increases.
  • Emitted particle: $^0_{-1}\beta$ with $A=0$, charge $-1$.
• Predicted nuclear changes
  • $Z$ increases by 1 (new proton).
  • $A$ unchanged (neutron becomes proton).
• Core equation (checked)
  • $^{14}<em>{6}\text{C} \;\rightarrow\; ^{14}</em>{7}\text{N} \; + \; ^0_{-1}\beta \; + \; \gamma$
  • Daughter isotope: Nitrogen-14.
• Additional practice
  • Iodine-131: $^{131}<em>{53}\text{I} \;\rightarrow\; ^{131}</em>{54}\text{Xe} \; + \; ^0_{-1}\beta$
  • Sodium-24: $^{24}<em>{11}\text{Na} \;\rightarrow\; ^{24}</em>{12}\text{Mg} \; + \; ^0_{-1}\beta$
• Real-world link: $^{14}\text{C}$ dating, medical tracers (I-131 for thyroid diagnostic/therapy).

Activity C – Proton → Neutron Processes

Positron Emission

• Internal change: Proton converts to neutron + positron + neutrino.
• Emitted particle: $^0_{+1}\beta$ (positron) with $A=0$, charge $+1$; followed by annihilation $\beta^+ + e^- \rightarrow 2\gamma$.
• Nuclear effect
  • $Z$ decreases by 1.
  • $A$ remains constant.
• Verified example (Carbon-11)
  • $^{11}<em>{6}\text{C} \;\rightarrow\; ^{11}</em>{5}\text{B} \; + \; ^0_{+1}\beta$
  • Daughter: Boron-11.
• Practice
  • Xenon-118: $^{118}<em>{54}\text{Xe} \;\rightarrow\; ^{118}</em>{53}\text{I} \; + \; ^0_{+1}\beta$
  • Manganese-50: $^{50}<em>{25}\text{Mn} \;\rightarrow\; ^{50}</em>{24}\text{Cr} \; + \; ^0_{+1}\beta$
• Medical relevance: PET scanning uses $\beta^+$ emitters (e.g., $^{11}\text{C}$, $^{18}\text{F}$).

Electron Capture (EC)

• Mechanism: Nucleus captures an inner-shell electron; proton + electron $\rightarrow$ neutron + neutrino; X-rays emitted as outer electrons fill the vacancy.
• Absorbed particle: $^0_{-1}e$ with $A=0$, charge $-1$.
• Nuclear effect identical to positron emission
  • $Z$ decreases by $1$, $A$ unchanged.
• Verified example (Tungsten-179)
  • $^{179}<em>{74}\text{W} + ^0</em>{-1}e \;\rightarrow\; ^{179}_{73}\text{Ta}$
  • Daughter: Tantalum-179.
• Practice
  • Gold-195: $^{195}<em>{79}\text{Au} + ^0</em>{-1}e \;\rightarrow\; ^{195}_{78}\text{Pt}$
  • Neodymium-141: $^{141}<em>{60}\text{Nd} + ^0</em>{-1}e \;\rightarrow\; ^{141}_{59}\text{Pr}$
• Comparison note: Positron emission & EC have the same net result ( $Z-1$ , $A$ constant); choice depends on nuclear energy balance.

Comparative Summary of Decay Modes

• Alpha ($\alpha$): $A-4,\;Z-2$; heavy, low range, high ionisation.
• Beta-minus ($\beta^-$): $A\text{ unchanged},\;Z+1$; moderate penetration.
• Beta-plus / Positron ($\beta^+$): $A\text{ unchanged},\;Z-1$; followed by annihilation $\gamma$.
• Electron capture: $A\text{ unchanged},\;Z-1$; internal X-ray emission.
• Gamma ($\gamma$): no change in $A$ or $Z$; accompanies other decays to shed excess energy.

Key Numerical & Conceptual Takeaways

• Mass number conservation: Sum of $A$ on both sides of an equation is equal.
• Charge/atomic-number conservation: Sum of $Z$ (including $-1$ for $\beta^-$, $+1$ for $\beta^+$, $-1$ for electron in EC) is conserved.
• Half-life (not directly in transcript but foundational): Time required for $50\%$ of a radioactive sample to decay; critical for carbon dating and medical dosage planning.
• Energy release: Mass–energy equivalence $E=mc^2$ explains why small mass defects in nuclear transformations yield large energies.

Ethical, Practical & Real-World Implications

• Medicine: Diagnostic imaging (PET, SPECT), cancer radiotherapy depend on controlled decay processes and understanding penetration/ionisation.
• Environmental health: Radon ($\alpha$ emitter) risk; nuclear waste management requires knowledge of long-lived beta/alpha emitters.
• Security & power: Alpha sources for RTGs in space probes; beta decay harnessed in betavoltaics; understanding decay crucial for nuclear reactors and weapons non-proliferation.

Connections to Foundational Principles

• Conservation laws (mass number, charge) mirror broader physics conservation of baryon number and electric charge.
• Subatomic transformations (n↔p) illustrate the weak nuclear force, one of the four fundamental interactions.
• Electron capture demonstrates overlap between atomic‐shell physics and nuclear processes, bridging quantum mechanics and nuclear chemistry.

Equations Toolbox (for quick revision)

• Alpha: $^{A}<em>{Z}\text{X} \;\rightarrow\; ^{A-4}</em>{Z-2}\text{Y} + ^4_2\text{He}$
• Beta-minus: $^{A}<em>{Z}\text{X} \;\rightarrow\; ^{A}</em>{Z+1}\text{Y} + ^0_{-1}\beta + \gamma$
• Beta-plus: $^{A}<em>{Z}\text{X} \;\rightarrow\; ^{A}</em>{Z-1}\text{Y} + ^0_{+1}\beta$
• Electron capture: $^{A}<em>{Z}\text{X} + ^0</em>{-1}e \;\rightarrow\; ^{A}_{Z-1}\text{Y}$

Study Tips

• Always balance both $A$ and $Z$; include the sign on $Z$ for electrons/positrons.
• Memorise the effect table (\alpha: $-4,-2$ ; $\beta^-$: $0,+1$ ; $\beta^+$ and EC: $0,-1$ ).
• Practise with periodic table open—identifying elements rapidly after $\Delta Z$ shifts accelerates problem solving.
• Remember that accompanying $\gamma$ emission does not alter $A$ or $Z$ but may appear in equations or experimental data.