Radioactivity and Nuclear Physics Fundamentals

24.1 Alpha-particles; Beta-particles, Gamma rays

Radioactivity is the process by which an unstable atomic nucleus loses energy by emitting radiation. This radiation can take several forms, primarily alpha particles, beta particles, and gamma rays, each with distinct properties.

Alpha Particles (α)

An alpha particle consists of two protons and two neutrons, identical to a helium nucleus (⁴He₂). They carry a positive charge of +2e and are relatively heavy. Due to their size and charge, alpha particles are easily stopped, even by a sheet of paper or the outer layer of skin. However, if ingested or inhaled, they can cause significant localized damage to biological tissues.

Beta Particles (β)

Beta particles are high-energy, high-speed electrons (β^-) or positrons (β⁺) emitted by certain types of radioactive nuclei. Beta-minus decay occurs when a neutron in the nucleus converts into a proton, emitting an electron and an antineutrino. Beta-plus decay involves a proton converting into a neutron, emitting a positron and a neutrino. Beta particles are lighter and have greater penetrating power than alpha particles, able to pass through several millimeters of aluminum but are stopped by thicker materials.

Gamma Rays (γ)

Gamma rays are high-energy electromagnetic radiation, similar to X-rays but with shorter wavelengths and higher frequencies. They are emitted from the nucleus when it transitions from an excited state to a lower energy state following an alpha or beta decay. Gamma rays have no mass or charge and are highly penetrating, requiring thick layers of lead or concrete to be attenuated significantly. They pose a significant external radiation hazard.

24.2 Laws of Radioactive Disintegration

The process of radioactive decay follows specific laws that describe how the number of unstable nuclei in a sample decreases over time.

Law of Radioactive Decay

The rate of radioactive decay is directly proportional to the number of undecayed nuclei present in the sample at any given time. Mathematically, this can be expressed as:

dN/dt = -λN

Where:

• dN/dt is the rate of decay (number of nuclei decaying per unit time)
• N is the number of undecayed nuclei present at time t
• λ (lambda) is the decay constant, a characteristic constant for a particular radioactive isotope. It represents the probability per unit time that a nucleus will decay.

Integrating this equation yields the number of undecayed nuclei at a given time:

N(t) = N₀e^-λt

Where:

• N(t) is the number of undecayed nuclei at time t
• N₀ is the initial number of nuclei at t = 0
• e is the base of the natural logarithm (approximately 2.718)

24.3 Half-life, Mean-life and Decay Constant

These three interrelated concepts are crucial for understanding the kinetics of radioactive decay.

Half-life (T_1/2)

The half-life of a radioactive isotope is the time required for half of the radioactive nuclei in a sample to decay. It is a fundamental characteristic of each isotope and is independent of the initial amount of the substance or external conditions like temperature or pressure.

T_1/2 = ln(2) / λ ≈ 0.693 / λ

After one half-life, 50% of the initial nuclei remain. After two half-lives, 25% remain, and so on.

Mean-life (τ)

The mean-life (or average-life) is the average lifetime of a radioactive nucleus before it decays. It is the reciprocal of the decay constant.

τ = 1 / λ

The mean-life is related to the half-life by:

τ = T_1/2 / ln(2) ≈ T_1/2 / 0.693 ≈ 1.44 T_1/2

Decay Constant (λ)

As discussed earlier, the decay constant is the probability per unit time that a nucleus will decay. A larger decay constant means a faster decay rate and a shorter half-life.

24.4 Geiger-Müller Tube

The Geiger-Müller tube, often referred to as a Geiger counter, is a widely used instrument for detecting and measuring ionizing radiation (alpha, beta, and gamma). It consists of a metal tube (cathode) with a thin wire (anode) running through its center, filled with an inert gas (e.g., argon) at low pressure and a small amount of quenching gas (e.g., alcohol vapor or halogen).

Principle of Operation

When an ionizing particle enters the tube, it collides with the gas atoms, ionizing them and producing free electrons and positive ions. The central wire is held at a high positive voltage relative to the tube wall. This strong electric field accelerates the free electrons towards the central wire. These accelerated electrons gain enough energy to cause further ionization of gas atoms, leading to an avalanche of electrons. This avalanche creates a measurable pulse of current, which is amplified and registered as a 'click' or a reading on a display. The quenching gas absorbs excess energy, preventing continuous discharge.

Limitations

• Cannot distinguish between different types of radiation (alpha, beta, gamma) without additional shielding.
• Has a 'dead time' after each pulse during which it cannot detect another particle, leading to inaccuracies at very high count rates.
• Inefficient for detecting high-energy gamma rays.

24.5 Carbon Dating

Carbon dating is a radiometric dating method that uses the naturally occurring radioactive isotope carbon-14 (¹⁴C) to determine the age of carbon-containing materials up to about 50,000 to 60,000 years old. It is widely used in archaeology, anthropology, and geology.

The Process

1. Formation of ¹⁴C: Cosmic rays interact with nitrogen atoms (¹⁴N) in the upper atmosphere, producing ¹⁴C.
2. Incorporation into Living Organisms: ¹⁴C, along with stable carbon isotopes (¹²C and ¹³C), is oxidized to carbon dioxide (CO₂). This CO₂ is then absorbed by plants through photosynthesis and subsequently transferred to animals through the food chain. Living organisms continuously exchange carbon with their environment, maintaining a relatively constant ratio of ¹⁴C to ¹²C in their tissues, similar to the atmospheric ratio.
3. Decay after Death: When an organism dies, it stops exchanging carbon with the environment. The ¹⁴C within its tissues then begins to decay back into ¹⁴N via beta decay, with a known half-life of approximately 5,730 years.
4. Age Determination: By measuring the remaining ratio of ¹⁴C to ¹²C in a sample and comparing it to the known atmospheric ratio, scientists can calculate how many half-lives have passed since the organism died, thereby determining its age.

Example Calculation

If an ancient wooden artifact has a ¹⁴C activity that is 25% of the activity found in a living tree, how old is the artifact?

Solution: 25% means two half-lives have passed (100% → 50% → 25%).

Age = 2 × 5,730 years = 11,460 years.

24.6 Medical Use of Nuclear Radiation and Possible Health Hazard

Nuclear radiation has found numerous beneficial applications in medicine, particularly in diagnosis and treatment. However, it also carries potential health risks that must be carefully managed.

Medical Uses

• Diagnostic Imaging:
  • PET Scans (Positron Emission Tomography): Uses positron-emitting radioisotopes (e.g., ¹⁸F) to create detailed 3D images of functional processes in the body, such as metabolism or blood flow, aiding in cancer detection, heart disease, and neurological disorders.
  • SPECT Scans (Single-Photon Emission Computed Tomography): Uses gamma-emitting radioisotopes (e.g., ^99mTc) to view organ function, blood flow, and bone activity.
  • X-rays and CT Scans: While not nuclear radiation in the strictest sense (they use external X-ray sources), they are closely related in principle and are essential for structural imaging.
• Radiation Therapy (Radiotherapy):
  • Uses high-energy radiation (gamma rays from ⁶⁰Co, X-rays from linear accelerators, or proton beams) to damage and destroy cancer cells. The goal is to target cancerous tissue while minimizing damage to healthy surrounding tissue.
  • Brachytherapy: Involves placing a radioactive source (e.g., ¹³¹I, ¹⁹²Ir) directly inside or next to the tumor.
• Sterilization of Medical Equipment: Gamma radiation is used to sterilize heat-sensitive medical devices, ensuring they are free from harmful microorganisms.

Possible Health Hazards

Exposure to nuclear radiation can cause various health effects, depending on the dose, type of radiation, and duration of exposure.

• Ionization and DNA Damage: Radiation can ionize atoms and molecules within cells, particularly DNA. This damage can lead to cell dysfunction, mutation, or cell death.
• Acute Radiation Syndrome (ARS): High doses of radiation (typically above 1 Gy) over a short period can cause severe illness with symptoms like nausea, vomiting, fatigue, hair loss, and compromised immune system function. Very high doses are lethal.
• Increased Cancer Risk: Even low doses of radiation increase the lifetime risk of developing cancer (e.g., leukemia, thyroid cancer). This is a stochastic effect, meaning the probability increases with dose, but not the severity.
• Genetic Defects: Radiation-induced damage to reproductive cells can lead to genetic mutations that may be passed on to offspring, although this risk is generally considered low in humans.
• Teratogenic Effects: Exposure during pregnancy can cause birth defects or developmental abnormalities in the fetus.

Radiation Protection Principles

To minimize risks, the ALARA principle (As Low As Reasonably Achievable) is followed, focusing on:

• Time: Minimize the duration of exposure.
• Distance: Maximize the distance from the source.
• Shielding: Use appropriate shielding materials (lead, concrete, water) to absorb radiation.