Comprehensive Guide to Radioactivity, Atomic Physics, and Nuclear Applications

Radioactivity Detection and Particle Identification

• Measuring Radioactivity: Ionising nuclear radiation is measured using a detector connected to a counter.

• Detection of Alpha Particles:

  • Alpha (\u03b1) particles are detected using a cloud chamber or a spark counter.

• Cloud Chambers:

  • There are several different types of cloud chambers used in radiation detection.
  • Internal Components and Set-Up:
    • A metal plate sits at the bottom, cooled using dry ice.
    • A transparent viewing film is placed at the top.
    • A light source is positioned at one side, allowing an observer to identify phenomena within the chamber.
    • A thin film of alcohol is evaporated inside the chamber, forming a vapour.
    • A radioactive source is placed within the chamber.
    • A magnetic field is applied at right angles to the chamber.
  • Mechanism of Action:
    • The vapour is obtained from cooling alcohol with dry ice.
    • When charged particles pass through the cloud chamber, they collide with gas molecules.
    • This creates ions around which the alcohol condenses, forming a visible path of condensation.
  • Identification of \u03b1-particles: They are identified by thick, short tracks that curl slowly in one direction.

• Spark Counters:

  • A spark counter consists of a thin metal gauze mounted very close (approximately $1\,mm$) to a thin wire.
  • A high voltage, typically around $5000\,V$, is applied across the gauze and the wire to induce sparking.
  • The voltage is reduced until sparking ceases.
  • When an alpha radiation source is brought near the gauze, it ionises the air, creating sparks between the gauze and the wire.

Count Rate and Geiger-M\u00fcller Detection

• Definition of Count Rate: The count rate is the number of decays per second recorded by a detector and displayed by a counter.

• Units of Measurement: It is measured in $\text{counts/s}$ or $\text{counts/min}$.

• Relationship with Distance: The count rate decreases as the detector moves further from the source because the radiation becomes more spread out.

• Detection of Beta (\u03b2) and Gamma (\u03b3) Radiation:

  • The Geiger-M\u00fcller tube (GM tube, GM detector, GM counter, or Geiger counter) is the most common device for measuring these types of radiation.
  • Mechanism: Every time the tube absorbs radiation, it transmits an electrical pulse to a counting machine. This results in a clicking sound or a digital display of the count rate.
  • Proximity Effects: A higher frequency of clicks or a higher count rate indicates more radiation absorption, which is directly affected by proximity to the source. Further distances result in lower detected count rates.

• Worked Example (Count Rate Calculation):

  • Scenario: A GM tube counts $16\,000$ decays in $1\,hour$.
  • Step 1: Identify variables: Number of decays = $16\,000$; Time = $1\,hour$.
  • Step 2: Convert time to seconds: $1\,hour = 60\,min \times 60\,s = 3600\,seconds$.
  • Step 3: Calculate rate: $\frac{16\,000}{3600} = 4.444...\,decays/s$. (Rounded to $4.5$ in the transcript).

Background Radiation: Natural and Artificial Sources

• Definition: Background radiation is the low-level radiation present all around us in the environment at all times.

• Variability: Levels vary significantly by geographic location.

• Natural Sources:

  • Radon Gas: Airborne radon comes from the ground due to the natural decay of uranium in rocks and soil. It is tasteless, colourless, and odourless. It is generally not a health issue unless concentrated.
  • Rocks and Buildings: Heavy elements like uranium and thorium occur naturally in rocks. Uranium decays into radon gas (an alpha emitter). This is dangerous if inhaled in large quantities. Building materials like stone, brick, and decorative rocks also contain natural radioactivity.
  • Cosmic Rays: The sun emits protons every second, some of which hit the Earth's atmosphere at high speeds. These collisions produce gamma radiation. Other sources include supernovae and high-energy cosmic events.
  • Carbon-14 (C-14): All organic matter contains a tiny amount of C-14. Living organisms constantly replace carbon, keeping the C-14 level constant during life.
  • Food and Drink: Radioactive elements from rocks and soil enter food and water. For example, bananas contain $Potassium-40$. The amounts are minuscule and not concerning.

• Man-Made (Artificial) Sources:

  • Medical Sources: X-rays, CT scans, radioactive tracers, and radiation therapy.
  • Nuclear Waste: Contributes little to overall background radiation but is hazardous for handlers.
  • Nuclear Fallout: Residuative radioactive material from weapons testing or explosions (e.g., Hiroshima). Current environmental levels are low but localized levels spike during tests.
  • Nuclear Accidents: Events like Chernobyl release large doses. While rare, they are catastrophic and can devastate areas for centuries.
  • Nuclear Power Contribution: Less than $0.1\%$ of total background radiation.

Accounting for Background Radiation

• Corrected Count Rate: In laboratory settings, background radiation must be subtracted from total readings to isolate the radiation from a specific source.

  • Procedure: Take a reading with no source present (background), then take the reading with the source. Subtract background from the total.

• Worked Example (Corrected Count Rate):

  • Scenario: A student measures counts at varying distances. Beyond $1\,metre$, the results stop changing.
  • Step 1: Determine the point where the source radiation is fully absorbed by the air. At $1\,metre$, the count rate stabilizes.
  • Step 2: Identify background: The constant reading after $1\,metre$ is the background rate, which is $15\,counts/min$.

The Nature of Radioactive Decay

• Process: Unstable nuclei emit high-energy particles or waves to become more stable.
• Energy Transfer: As radiation moves away, it carries energy, reducing the overall energy of the nucleus and increasing stability.
• Spontaneous Process: Decay cannot be affected by environmental factors like temperature, pressure, or chemical conditions.
• Random Process: It is impossible to know exactly when a specific nucleus will decay or in which direction the radiation will be emitted.

Properties of Alpha, Beta, and Gamma Radiation

• Alpha (\u03b1) Particles:

  • Nature: Identical to a helium nucleus (two protons and two neutrons).
  • Charge: $+2$.
  • Range in Air: A few centimetres ($cm$).
  • Penetration: Stopped by a sheet of paper.
  • Ionising Effect: High.

• Beta (\u03b2-) Particles:

  • Nature: Fast-moving electrons.
  • Origin: Produced in nuclei when a neutron changes into a proton and an electron.
  • Charge: $-1$.
  • Range in Air: A few tens of centimetres ($cm$).
  • Penetration: Stopped by a few millimetres ($mm$) of aluminium.
  • Ionising Effect: Medium.

• Gamma (\u03b3) Radiation:

  • Nature: High-energy electromagnetic wave.
  • Charge: $0$ (no charge).
  • Range in Air: Infinite.
  • Penetration: Reduced by a few millimetres ($mm$) of lead.
  • Ionising Effect: Low.

• Trends: Moving from Alpha to Gamma, range and penetrating power increase, while ionising power decreases.

Deflection in Electric and Magnetic Fields

• Prerequisite for Deflection: A particle must have a charge to be deflected by an electric field, and must be moving perpendicular to a magnetic field to be deflected by it.

• Electric Field Behavior:

  • Alpha particles ($+2$ charge) move toward the negative plate. They are heavier, so they deflect less.
  • Beta particles ($-1$ charge) move toward the positive plate. They are lighter, so they deflect more.
  • Gamma rays (no charge) travel straight through.

• Magnetic Field Behavior:

  • Alpha and Beta particles are deflected in opposite directions because of their opposite charges.
  • Gamma radiation is not deflected.

Radioactive Decay Equations

• Conservation Laws: The sum of mass numbers (top) and atomic numbers (bottom) must be equal on both sides of the equation.

• Alpha Decay:

  • The mass number decreases by $4$.
  • The atomic number decreases by $2$.
  • Example: ${}^{212}_{84}\text{Po} \rightarrow {}^{208}_{82}\text{Pb} + {}^{4}_{2}\text{He}$.

• Beta Decay:

  • A neutron changes to a proton (stays in nucleus) and an electron (emitted).
  • The mass number remains the same.
  • The atomic number increases by $1$.

• Gamma Decay:

  • Emission of high energy with no mass or charge.
  • Mass number and atomic number remain unchanged.
  • Example: ${}^{238}_{92}\text{U} \rightarrow {}^{238}_{92}\text{U} + \gamma$.

Nuclear Fission and Fusion

• Nuclear Fission:

  • Definition: The splitting of a large, unstable nucleus into two smaller daughter nuclei.
  • Fuel: Isotopes of uranium ($U-235$) and plutonium are commonly used.
  • Process: A neutron collides with the unstable nucleus, causing it to split. This releases two or three neutrons and gamma rays.
  • Energy: Energy is transferred from nuclear potential energy to kinetic energy of the products. The total mass of products is slightly less than the original mass, as the missing mass is converted to energy.

• Nuclear Fusion:

  • Definition: Two light nuclei join to form a heavier nucleus.
  • Requirements: Extremely high temperatures are needed to maintain the process.
  • Natural Example: Stars use fusion (hydrogen to helium) to produce energy.
  • Energy Efficiency: $1\,kg$ of hydrogen via fusion provides energy equivalent to $10\,million\,kg$ of coal.
  • Equation: Einstein's mass-energy equivalence $E = mc^2$, where $E$ is energy ($J$), $m$ is mass converted ($kg$), and $c$ is the speed of light ($m/s$).

Chain Reactions

• Mechanism: One neutron induces fission in a $U-235$ nucleus, which releases $2-3$ more neutrons. These neutrons then trigger further fissions.
• Controlled Chain Reaction: In nuclear reactors, some neutrons are removed to keep the frequency constant. Control rods are used to absorb neutrons without becoming unstable themselves.
• Uncontrolled Chain Reaction: Used in nuclear weapons to release massive energy in a short burst (explosion).

Half-Life and Radioactive Dating

• Definition of Half-Life: The time taken for half the nuclei of an isotope in a sample to decay, or the time for activity to fall to half its original level.
• Characteristics: Constant for a specific isotope; can range from fractions of a second to billions of years.
• Carbon-14 Dating:
  • Process: Cosmic rays create C-14 by hitting nitrogen in the air. Plants absorb it via photosynthesis; animals eat the plants.
  • Post-Death: Absorption stops. C-14 decays with a half-life of approximately $5730\,years$.
  • Reliability: Most reliable for samples between $1000$ and $40\,000\,years$ old.
    • If $< 1000\,years$: Change in activity is too small to measure accurately.
    • If $> 40\,000\,years$: Remaining C-14 activity is too low, similar to background radiation.

Practical Applications of Radiation

1. Smoke Detectors: Use alpha particles to ionise air, creating a current. Smoke blocks the alpha particles, breaking the current and triggering the alarm.
2. Thickness Control: Beta particles are used for thin materials (paper, aluminium foil). Thicker material absorbs more beta, thinner allows more through; the detector adjusts the machinery accordingly. Alpha would be fully absorbed; Gamma would not show enough difference.
3. Sterilisation: Gamma rays kill bacteria on food (making it last longer) and medical equipment (can irradiate through packaging). Irradiated food often carries the Radura symbol.
4. Radiotherapy: Intense gamma beams kill cancer cells. Beams are rotated to minimize damage to healthy tissue.
5. Tracers: Radioactive isotopes track movement (e.g., blood) in the body. PET scans detect these emissions for diagnosis.

Safety and Dangers of Radioactivity

• Biological Risks: Cell death, tissue damage, DNA mutations, and cancer.
• Mutations: Ionisation of DNA can lead to faulty repair and replication, forming tumours.
• Acute Symptoms: Skin burns (similar to sunburn) and reduced white blood cell count (weakened immune system).
• Safe Handling Procedures:
  • Store sources in lead-lined boxes.
  • Handle for the minimum time necessary.
  • Use long-handled tongs to keep sources at a distance.
  • Gloves and safety specs are used if there is a leakage risk.
  • Keep accurate records of usage (date and time).
• Waste Disposal: Isotopes with long half-lives remain dangerous for millennia and are buried deep underground in specialized containers.