Ch7: Radioactivity

Discovery & Historical Context

  • Radioactivity discovered by a female scientist
    → Marie Curie.
  • Awarded two separate Nobel Prizes (Physics and Chemistry).
  • Established that radiation originates inside the atom, not from chemical processes.

What Makes An Element Radioactive?

  • Radioactive = unstable nucleus that spontaneously emits radiation.
  • Key factor: neutron-to-proton ratio (N/Z).
  • Large imbalance (too many neutrons) o instability.
  • Elements with Z \ge 84 (Polonium and beyond) are invariably radioactive.
  • Unstable nuclei undergo successive decays until a stable N/Z ratio is reached.

Types of Nuclear Radiation

  • Alpha (α) particles
    • Composition: ^4_2\text{He} (2 p, 2 n).
    • Charge: +2; relatively heavy.
    • Mass number of parent nucleus decreases by 4; atomic number by 2.
    • Stopped by a sheet of paper or skin.
  • Beta (β) particles
    • Composition: ^0_ {-1}e (electron) or positron variant ^0_{ +1}e (not covered here).
    • Charge: -1; negligible mass.
    • In nucleus, a neutron o proton + electron.
    • Atomic number increases by 1; mass number unchanged.
    • Penetration: a few mm of aluminum/plastic.
  • Gamma (γ) rays / photons
    • Pure electromagnetic energy; \text{no mass, no charge}.
    • Emission often follows α or β decay to shed excess energy.
    • No change to A or Z of the emitting nucleus.
    • High penetration; needs thick lead/concrete shielding.

Nuclear vs Electromagnetic Radiation (Contextual Clues)

  • Electromagnetic (EM) radiation is light-like and usually originates in electronic transitions or the Sun.
  • Nuclear radiation originates in the nucleus of an isotope.
  • Classification examples from lecture:
    • “Gamma from cobalt-60 to destroy tumors” o Nuclear (product of ^{60}\text{Co} decay).
    • “Watch out for UV rays from the Sun” o EM.
    • “Rutherford detected radiation from uranium” o Nuclear.

Energy–Wavelength Relationship

  • Shorter wavelength \Rightarrow higher frequency \Rightarrow higher energy E = h\nu.
  • Radiation shorter than visible (\sim 400\, \text{nm}) includes:
    • Ultraviolet (UV), X-rays, γ-rays (highest energy).

Balancing Nuclear Equations (Method & Examples)

General rule: Sum of superscripts (mass numbers, A) and subscripts (atomic numbers, Z) must be equal on both sides.

Example 1 – Unknown X Found to be an α Emitter

  • Skeleton: ^{92}_ ?\text{U} \to ^{?}_ ?\text{Ra} + X.
  • Matching totals gave X = ^{4}_2\text{He} \to α particle.

Example 2 – β-Decay of ^{234}_ {90}\text{Th}

  • Equation: ^{234}_ {90}\text{Th} \to ^{234}_ {91}\text{Pa} + ^0_ {-1}e.
  • Check: A: 234 = 234+0, Z: 90 = 91+(-1).

Example 3 – β-Decay of Rubidium-86

  1. Write parent: ^{86}_ {37}\text{Rb}.
  2. Add β particle: ^{0}_ {-1}e.
  3. Balance Z: new nucleus has Z = 37 - (-1) = 38.
  4. Balance A: stays 86.
  5. Nuclear product: ^{86}_ {38}\text{Sr} (strontium-86).
  6. Final equation: ^{86}_ {37}\text{Rb} \to ^{86}_ {38}\text{Sr} + ^0_ {-1}e.

Example 4 – α-Decay of Plutonium-239

  • Parent: ^{239}_ {94}\text{Pu}.
  • α particle: ^{4}_2\text{He}.
  • Product nucleus:
    • A = 239 - 4 = 235.
    • Z = 94 - 2 = 92 \to Uranium.
  • Equation: ^{239}_ {94}\text{Pu} \to ^{235}_ {92}\text{U} + ^4_2\text{He}.

Gamma Emission Reminder

  • If \gamma is emitted: A and Z do not change.

Health & Dosimetry

  • Radiation dose often expressed in rem or Sievert (1\,\text{Sv} \approx 100\,\text{rem}).
  • Approximate biological effects (annual exposure):
    • <25\,\text{rem}: No observable effect.
    • >25\,\text{rem}: Drop in white-blood-cell count.
    • Several hundred rem: Acute radiation sickness; \ge 500\,\text{rem} can be fatal.
  • Pie-chart of common exposure sources (approximate):
    • \sim 55\% Radon gas in homes.
    • \sim 11\% Medical X-rays.
    • \sim 4\% Nuclear medicine, etc.

Medical & Pharmaceutical Relevance

  • Radioisotopes (e.g. ^{60}\text{Co} \gamma-rays) used in cancer therapy.
  • Drug design must consider half-life concept (same mathematical description as nuclear decay) to maintain therapeutic levels without prolonged radiation inside body.

Protection Strategies (ALARA Principle)

  • Time: Minimize exposure duration.
  • Distance: Inverse-square law, I \propto 1/r^2 – step back when possible.
  • Shielding: Use material matched to radiation type:
    • Paper or skin for α.
    • Aluminum/plastic for β.
    • Thick lead/concrete for γ.

Summary Cheat-Sheet

  • α: ^4_2\text{He} \downarrow A=4, \downarrow Z=2, low penetration.
  • β: ^0_ {-1}e \uparrow Z=1, A steady, moderate penetration.
  • γ: h\nu, only energy, high penetration, no change in A, Z.
  • Radioactive if unstable N/Z; all Z\ge84.
  • Balance nuclear equations by conserving A and Z.