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 $Z$.