Chapter 8 - Particles in the Nucleus

8.1 Atoms, Isotopes and Radioisotopes

• Earth is naturally radioactive; we are constantly exposed to background radiation.

• Human senses cannot detect radiation, but our bodies are adapted to low levels. High doses can be damaging.

• Radioactive atoms (radioisotopes) have beneficial uses (e.g., medicine).

The Standard Model

• All matter is composed of 12 fundamental particles (fermions): 6 quarks and 6 leptons.

• These are not seen in everyday situations; produced in high-energy particle accelerators.

• Quarks (make up hadrons like protons & neutrons): up (u), down (d), charm (c), strange (s), top (t), bottom (b).

• Leptons: electron (e⁻), muon (μ⁻), tau (τ⁻), and their neutrinos (ν_e, ν_μ, ν_τ).

• Hadrons = particles made of quarks (baryons = 3 quarks; mesons = quark + antiquark).

  • Proton = uud (2 up + 1 down).

  • Neutron = udd (1 up + 2 down).

Fermions Table (masses relative to proton):

• Quarks: Fractional charges (+2/3 or –1/3).

• Leptons: Electron, muon, tau have charge –1; neutrinos have charge 0.

Antiparticles:

• Same mass, opposite charge (or opposite quantum numbers).

• Example: positron (e⁺) is antiparticle of electron.

The Structure of Atoms

• Atoms consist of a tiny, dense nucleus (protons + neutrons = nucleons) surrounded by an electron cloud.

• Nucleus contains >99% of atom’s mass but is extremely small (~10⁻¹² of atom’s volume).

• Atomic notation: ^A_ZX

  • Z (atomic number) = number of protons.

  • A (mass number) = protons + neutrons (nucleons).

  • Neutrons (N) = A – Z.

Electrically neutral atom: Number of electrons = number of protons (Z).

Isotopes

• Atoms of the same element (same Z) but different number of neutrons (different A).

• Same chemical properties, different physical properties (e.g., density, mass).

• Nuclide: Refers to a specific nucleus.

• Hydrogen isotopes:

  • Protium (¹H): 1 proton, 0 neutrons.

  • Deuterium (²H): 1 proton, 1 neutron.

  • Tritium (³H): 1 proton, 2 neutrons.

Worked Example Highlights:

• For ¹⁹⁷₇₉Au: Z=79 (protons), A=197 (nucleons), N=118, electrons=79.

• Isotopes have same Z, different N and A.

Radioisotopes

• Unstable isotopes that undergo spontaneous transmutation (emit radiation/particles and change into different element/isotope).

• Most atoms are stable; only certain combinations of protons & neutrons are stable.

• Radioactive if nucleus is unstable (naturally occurring or artificial).

• Symbol: Radiation warning trefoil (Figure 8.1.11).

• Periodic table: All isotopes of elements with Z > 83 (bismuth) are radioactive; many lighter elements have radioactive isotopes (shaded yellow in Figure 8.1.12).

Artificial Transmutation: How Radioisotopes Are Manufactured

• Most radioisotopes (~3000) are produced artificially (only ~270 occur naturally).

• Common method: Neutron absorption in a nuclear reactor.

  • Stable isotope + neutron → radioactive isotope.

• Example: Cobalt-59 (stable) + neutron → Cobalt-60 (radioactive, used in medicine).

• Produced in facilities like ANSTO (Lucas Heights, Sydney) using nuclear reactors.

Stability of Nuclei and Why Radioactive Nuclei Are Unstable

• Strong nuclear force (mediated by gluons) holds nucleus together — very strong but short-range.

• Electrostatic repulsion between protons tries to break nucleus apart.

• Line of stability (Figure 8.1.15): Stable nuclei cluster around a curved line (N ≈ Z for light elements; N > Z for heavier elements).

• For stability, neutrons help “dilute” proton repulsion.

• Unstable nuclei (away from line) emit radiation (α, β⁻, β⁺) to reach stability.

• Bismuth-209 is the heaviest stable isotope; heavier nuclei are unstable.

Examples:

• Small balanced nuclei (e.g., carbon-12) are stable.

• Large nuclei with too many protons or neutrons become unstable.

8.2 Radiation

• Early researchers (Marie Curie, Ernest Rutherford, Paul Villard) discovered three types of radiation: alpha (α), beta (β), and gamma (γ).

• Alpha & beta are particles emitted from the nucleus.

• Gamma is high-energy electromagnetic radiation.

• Radioactive decay: Process where unstable nucleus emits particles/radiation.

Alpha (α) Decay

• Occurs in heavy unstable nuclei.

• Emits an alpha particle (⁴₂α or ⁴₂He²⁺): 2 protons + 2 neutrons (helium nucleus).

• Nuclear equation example (Uranium-238): ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂α + energy

• Parent nucleus → daughter nucleus (different element = nuclear transmutation).

• Atomic number decreases by 2; mass number decreases by 4.

• Energy released mostly as kinetic energy of the fast-moving alpha particle.

Conservation: Atomic number (Z) and mass number (A) are conserved in nuclear reactions.

Beta (β) Decay

Beta-Minus (β⁻) Decay

• Occurs when nucleus has too many neutrons.

• A neutron changes into a proton + electron (β⁻) + antielectron neutrino (ν̅_e).

• Example (Carbon-14): ¹⁴₆C → ¹⁴₇N + ⁻¹₀β + ν̅_e + energy

• Atomic number increases by 1; mass number unchanged.

• Beta particle is a high-energy electron from the nucleus.

Beta-Plus (β⁺) Decay

• Occurs when nucleus has too many protons.

• A proton changes into a neutron + positron (β⁺) + electron neutrino (ν_e).

• Example: ¹²₆C → ¹²₅B + ¹₀β⁺ + ν_e

• Atomic number decreases by 1; mass number unchanged.

• Positron (β⁺) is the antiparticle of the electron (positive charge).

Gamma (γ) Decay

• High-energy electromagnetic radiation (no mass, no charge).

• Emitted when daughter nucleus is in an excited state after α or β decay.

• Releases excess energy; nucleus rearranges to more stable state.

• Example (Iodine-131 decay sequence): Beta decay → excited Xenon-131 → stable Xenon-131 + γ

• No change in atomic or mass number.

• Travels at speed of light.

Conservation Laws in Nuclear Reactions

• Mass-energy: Total energy (rest mass + kinetic) is conserved (E = mc²).

• Charge: Total charge before = total charge after.

• Momentum: Total momentum before = total after.

• Atomic and mass numbers are always conserved.

Worked Example Insight: Energy differences in decays are calculated in MeV (mega-electron volts).

Range of Energies for Different Radiations

• Alpha particles: 5–10 MeV (or MeV range).

• Beta particles: Up to a few MeV.

• Gamma rays: Typically < 1 MeV (e.g., up to 412 keV for gold-198).

Higher energy → greater speed/frequency (for gamma).

Detection of Radiation

• Human senses cannot detect it.

• Geiger Counter (Geiger-Müller tube):

  • Filled with argon gas.

  • High voltage between electrodes.

  • Radiation ionises gas → current pulse → audible click.

• Used for mineral exploration, safety monitoring, medical/industrial checks.

Physics in Action: How Technetium-99m is Produced

• Most widely used radioisotope in nuclear medicine (cancer diagnosis/treatment).

• Produced from Molybdenum-99 (from Lucas Heights reactor) via beta-minus decay: ⁹⁹₄₂Mo → ⁹⁹ᵐ₄₃Tc + ⁻¹₀β + ν̅_e

• Tc-99m then emits gamma ray: ⁹⁹ᵐ₄₃Tc → ⁹⁹₄₃Tc + ⁰₀γ

• Short half-life → produced on-site in hospital generators (lead-shielded).

8.3 Properties of Alpha, Beta and Gamma Radiation

• Early experiments (with radium) using a magnetic field showed three distinct types of radiation (Figure 8.3.1):

  • Alpha (α): Deflected one way (positively charged).

  • Beta (β): Deflected the opposite way (negatively charged).

  • Gamma (γ): Not deflected (no charge).

• Differences in charge, mass, and speed.

Speed and Charge

Alpha (α) Particles (Figure 8.3.2)

• Consist of 2 protons + 2 neutrons (helium nucleus, ⁴₂He²⁺).

• Charge: +2.

• Mass: Relatively heavy.

• Speed: Slow — up to 20,000 km/s (about 0.1c or 10% speed of light).

Beta-Minus (β⁻) and Beta-Plus (β⁺) Particles (Figure 8.3.3)

• β⁻: Fast-moving electrons (negative charge).

• β⁺: Positrons (positive charge, antiparticle of electron).

• Mass: Very light (much lighter than alpha).

• Speed: Very fast — up to ~90% speed of light (0.9c).

Gamma (γ) Rays (Figure 8.3.5)

• High-energy electromagnetic radiation (part of EM spectrum, Figure 8.3.4).

• Charge: 0 (no charge).

• Mass: None (no rest mass).

• Speed: Speed of light (3.00 × 10⁸ m/s).

Penetration Ability and Ionisation

Alpha (α) Particles (Figure 8.3.6)

• High ionising ability: Strongly interact with atoms, knock off electrons, create ions.

• Low penetration: Travel only a few centimetres in air; stopped by paper, skin, or thin card.

• Easily absorbed — become helium atoms after gaining electrons.

Beta (β) Particles (Figure 8.3.8)

• Low ionising ability: Fewer interactions due to smaller charge and higher speed.

• Moderate penetration: Travel a few metres in air; stopped by a few mm of aluminium or thin metal/plastic sheet.

• Can pass through skin but stopped by thin metal.

Gamma (γ) Rays

• Very low ionising ability: Weak interaction with matter (only ionise if direct collision).

• High penetration: Travel long distances in air; penetrate through human body, aluminium sheets, and several cm of lead (thick lead or concrete needed to stop).

Summary Table 8.3.1: Comparison of Properties

Physics in Action: Applications

Monitoring Thickness of Sheet Metal (Figure 8.3.10)

• Beta-minus particles used.

• Source under sheet; detector above.

• Fewer beta particles reach detector if sheet is thicker → adjusts rollers automatically.

Gamma Knife Therapy (Figure 8.3.11)

• Focused gamma beams from many directions target bra

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• in tumours.

• High dose at tumour; surrounding tissue receives low dose.

Smoke Detectors

• Use alpha emitter (e.g., Americium-241) — alpha particles ionise air; smoke reduces current, triggers alarm.

8.4 Half-Life and Decay Series

• Different radioisotopes decay at different rates.

• Activity: Rate of radioactive decay (measured by Geiger counter as counts per second).

• Example:

  • Polonium-218: High initial activity, drops rapidly (almost zero in ~30 minutes).

  • Uranium-235: Low activity, remains almost constant over decades (Figure 8.4.1).

Half-Life (t₁_/₂)

• Definition: Time taken for half of the radioactive nuclei in a sample to decay.

• Half-life is constant for a given radioisotope and cannot be changed by chemical reactions, heat, etc.

• Determined only by nuclear instability.

• Example: Polonium-218 has t₁/₂ ≈ 3.10 minutes.

Mathematical Formula:

• Number of nuclei remaining:

• Number of half-lives:

Decay Curve: Exponential decay — activity halves

with each half-life.

Worked Example Insight:

• After each half-life, activity and number of nuclei halve (100% → 50% → 25% → 12.5%, etc.).

Activity (A)

• Activity (A): Number of disintegrations per second (measured in becquerels, Bq). 1 Bq = 1 disintegration/second.

• Formula:

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• Activity also follows:

Worked Example Insight:

• Technetium-99m (short half-life) activity drops rapidly — useful for medical imaging.

Common Radioisotopes and Their Applications (Table 8.4.1)

Decay Series

• Decay of a radioisotope often produces another radioactive daughter nucleus → continues until a stable isotope is reached.

• Decay series: Sequence of decays (Figure 8.4.4 shows Uranium-238 series).

• Uranium-238 series ends at stable Lead-206.

• Earth is old enough (4.5 billion years) that only 4 natural decay series remain active (Uranium, Actinium, Thorium, Neptunium).

Applications:

• Rock dating: Measure proportions of radioactive elements and daughters in rocks.

Extension: Radiocarbon Dating33

• Uses Carbon-14 (t₁/₂ = 5730 years, β⁻ decay to Nitrogen-14).

• Living organisms have constant C-14/C-12 ratio (from atmosphere).

• After death, C-14 decays and is not replaced → ratio decreases.

• Compare C-14/C-12 ratio to estimate age (accurate up to ~60,000 years).

• Examples: Shroud of Turin (medieval), mammoth fossils.

8.5 Radiation Doses and Effects on Humans

• We are constantly exposed to low-level background radiation (natural sources).

• High exposure from α, β, γ sources (medicine, industry, nuclear power) can be harmful.

• Monitoring is essential for workers (radiologists, nuclear plant staff) and patients (cancer treatment).

• Dosimeters measure personal exposure

Ionising Radiation

• Ionising radiation: High-energy EM radiation (frequency > 2.00 × 10¹⁶ Hz) that can remove electrons from atoms, creating ions (Figure 8.5.3).

  • Includes: Gamma rays, X-rays, and some UV.

• Non-ionising radiation: Lower energy (radio waves, microwaves, visible light, infrared, UV-A) — generally harmless in everyday amounts (Figure 8.5.2).

Effects of Ionisation:

• Breaks chemical bonds in molecules (e.g., water → ions).

• Can damage cells, cause cancer, or lead to radiation sickness.

Measuring Radiation Exposure

Absorbed Dose (AD)

• Energy absorbed per kilogram of tissue.

• Formula:

• Unit: Gray (Gy) → 1 Gy = 1 J/kg.

Dose Equivalent (DE)

• Accounts for the type of radiation (different biological damage).

• Formula: DE = AD × QF (QF = quality factor / weighting factor).

• Unit: Sievert (Sv) or millisievert (mSv), microSievert (μSv).

Quality Factors (Table 8.5.1):

• α particles: 20 (highly damaging due to high charge, mass, low speed).

• Neutrons (10 keV): 10.

• β particles, γ rays, X-rays: 1.

Background Radiation

• Average annual exposure in Australia: ~1.5 mSv.

• Sources (Figure 8.5.4 & 8.5.6):

  • Natural (~90%): Cosmic rays, rocks/soil, food/drink, radon gas, natural radioactivity in air.

  • Artificial: Medical (X-rays), nuclear power, etc.

• Background radiation is low and generally not harmful.

Effect of Radiation Exposure on Humans

• Symptoms: Nausea, fatigue, hair loss, reduced white blood cells, cancer risk.

• Rapidly dividing cells (cancer, bone marrow) are most vulnerable.

Medical Applications of Radiation

• Cancer treatment: Targeted radiation (e.g., cobalt-60) damages cancer cells more than healthy tissue (Figure 8.5.8).

• Radioactive tracers (Table 8.5.5): Short half-life isotopes injected/ingested to image organs.

• Scintigraphy: Gamma camera detects tracer emissions to create images (Figure 8.5.10).

Typical Medical Exposures (Table 8.5.4):

• Chest X-ray: 30 μSv.

• CT scan: 5000 μSv.

• Radiotherapy course: Very high (targeted).

Physics in Action: Scintigraphy

• Uses radioactive tracers with same chemical properties as stable isotopes.

• Tracer emits gamma rays → detected to map organ function.

Dosimeters (Figure 8.5.5):

• Thermoluminescent dosimeters (TLDs) used by workers for accurate monitoring.