IP Physics Notes (Upper Secondary, Year 3-4): 17) Radioactivity

Quick recap -- Unstable nuclei shed energy by emitting alpha, beta, or gamma radiation. Identify the emission, update the nuclide notation, and use half-life reasoning to track activity changes.

Rutherford Scattering Recap

• Most alpha particles passed straight through gold foil -> atoms mostly empty space.
• Some deflected at large angles -> positive charge concentrated in tiny nucleus.
• A few rebounded -> nucleus is dense and carries most mass.
• Led to nuclear model: central nucleus (protons + neutrons) with orbiting electrons.

Nuclear Notation & Isotopes

• Nuclide represented as \( ^A_Z \text{X} \) where \( A \) is nucleon number, \( Z \) proton number.
• Isotopes share \( Z \) but have different neutron counts (different \( A \)).
• Proton number defines element; neutron-proton balance determines stability.

Types of Radioactive Emission

Nuclear Equations

• Alpha decay \( \alpha\) or \(\text{He}^{2+}\): \[ ^A_Z \text{X} \to \space ^{A-4}_{Z-2} \text{Y} + \space ^4_2 \text{He} \]
• Beta decay \(\beta\) or \(\text{e}^-\):
  \[ \begin{aligned} \text{neutron } n &\to& \text{proton } p^+ &\space&+&\space& \text{electron } e^- &\space&+&\space& \text{antineutrino } \overline{\nu} \\ ^A_Z \text{X} &\to& ^A_{Z+1} \text{Y} &\space&+&\space& ^0_{-1} \beta &\space&+&\space& \overline{\nu} \end{aligned} \]
• Gamma emission accompanies other decays; no change to \( A \) or \( Z \); nucleus transitions to lower energy state.

Half-Life & Activity

• Half-life \( T_{1/2} \): time for activity or number of undecayed nuclei to halve.
• After \( n \) half-lives: remaining fraction \( = \left( \frac{1}{2} \right)^n \).
• Activity \( A \) (decays per second) proportional to number of undecayed nuclei.

Worked Example: Half-Life Count

A sample starts with activity \( \pu{6400 Bq} \). If half-life is \( \pu{12 h} \), find activity after \( \pu{36 h} \).

\[ 36 h = 3 \times 12 h \Rightarrow n = 3 \text{ half-lives}.\quad A = 6400 \left( \dfrac{1}{2} \right)^3 = \pu{800 Bq}. \]

Detecting Radiation

• Geiger-Mller tube: ionising radiation makes gas conductive; pulses counted.
• Photographic film: darkens under exposure.
• Scintillation detectors: light flashes converted to electrical signals.
• Always subtract background count when analysing data.

Applications & Risks

• Medical tracers (short half-life beta/gamma emitters).
• Radiotherapy (gamma/x-rays) for tumour destruction.
• Industrial thickness control (beta sources), smoke detectors (alpha sources).
• Hazards: ionisation of living tissue causing burns, cancer, or genetic damage.
• Safety: shielding, distance, minimised exposure time, proper storage, monitoring badges.

Key Takeaways

• Use nuclide notation carefully when balancing decay equations.
• Half-life problems often hinge on counting discrete halving steps; convert times accordingly.
• Gamma accompanies other emissions to shed excess energy; it doesn't alter \( A \) or \( Z \).
• Always mention safety protocols when discussing uses of radioactive sources.