Unit 24: Radioactivity and Nuclear Reaction

Introduction

Radioactivity is the spontaneous emission of particles or electromagnetic radiation from unstable atomic nuclei. Understanding the different types of radiation, their properties, and how they interact with matter is essential for applications ranging from archaeological dating to cancer treatment. This chapter provides a detailed examination of alpha, beta, and gamma rays, the laws that describe radioactive disintegration, and practical tools and techniques that harness or measure radioactivity.

Alpha, Beta and Gamma Rays

Three primary forms of nuclear radiation are distinguished by their composition, charge, and penetrating ability.

Alpha (α) Particles

Composition: Helium nucleus consisting of 2 protons and 2 neutrons (^4_2He).
Charge: +2e (positive).
Penetrating Power: Least penetrating; stopped by a sheet of paper or the outer layer of human skin.
Applications: Used in smoke detectors (americium-241 source) and as a source of helium in certain scientific experiments.

Beta (β) Particles

Composition: High‑speed electrons (β⁻) or positrons (β⁺) emitted from the nucleus.
Charge: –1e for electrons, +1e for positrons.
Penetrating Power: Moderate; can penetrate paper but are stopped by a few millimetres of aluminium or plastic.
Applications: Employed in radiotherapy (e.g., strontium‑90 for eye treatments) and as tracers in biochemical research.

Gamma (γ) Rays

Composition: Electromagnetic photons (no mass, no charge).
Charge: Neutral.
Penetrating Power: Most penetrating; requires dense shielding such as lead (several centimetres) or concrete to attenuate significantly.
Applications: Used in sterilisation of medical equipment, cancer radiotherapy (gamma knife), and industrial radiography.

Despite their differences, all three types of radiation originate from nuclear transitions and obey the same statistical laws of decay.

Laws of Radioactive Disintegration

The decay of a radioactive sample follows exponential statistics, which can be expressed through two fundamental equations.

Decay Law

The number of undecayed nuclei N at time t is given by:

N = N_0 e^{-\lambda t}

where:

N_0 = initial number of radioactive nuclei at t = 0,
\lambda = decay constant (probability per unit time that a nucleus will decay),
t = elapsed time.

Activity (Decay Rate)

The activity A, defined as the number of decays per unit time, is:

A = \lambda N = A_0 e^{-\lambda t}

with A_0 = \lambda N_0 being the initial activity. Activity is measured in becquerels (Bq), where 1 Bq = 1 decay per second.

Half‑Life, Mean Life and Decay Constant

These interrelated quantities characterize the timescale of radioactive decay.

Half‑Life (`t_{1/2}`)

The time required for half of the radioactive nuclei in a sample to decay:

t_{1/2} = \frac{0.693}{\lambda}

Derivation: set N = N_0/2 in the decay law and solve for t.

Mean Life (`\tau`)

The average lifetime of a radioactive nucleus before decay:

\tau = \frac{1}{\lambda} = 1.44\, t_{1/2}

The factor 1.44 arises from the integral of the exponential decay function.

Decay Constant (`\lambda`)

The probability per unit time that a given nucleus will decay:

\lambda = \frac{0.693}{t_{1/2}}

A larger \lambda corresponds to a shorter half‑life and a more rapidly decaying nuclide.

Geiger‑Muller (GM) Tube

The Geiger‑Muller tube is a widely used device for detecting and measuring ionising radiation.

Working Principle

The tube is filled with a low‑pressure inert gas (e.g., argon) mixed with a quenching agent.
When radiation enters the tube, it ionises gas molecules, creating electron‑ion pairs.
A high voltage (~400–600 V) applied between the central anode and the cylindrical cathode accelerates these electrons, causing an avalanche of secondary ionisations.
The resulting pulse of charge is collected by the anode, producing a measurable voltage spike.
Each pulse corresponds to a single detection event; the pulse rate is proportional to the radiation intensity.

Detection Capabilities

Radiation Type	Detectability by GM Tube	Comments
Alpha	Yes (if window is thin enough)	Requires a thin mica or polymer window; otherwise alpha particles are stopped by the tube wall.
Beta	Yes	Easily detected; moderate penetration allows entry through the tube wall.
Gamma	Yes (with lower efficiency)	Gamma photons interact via Compton scattering or photoelectric effect within the gas; efficiency depends on tube dimensions and gas pressure.

Applications

Radiation surveys in laboratories and nuclear facilities.
Personal dosimetry and safety monitoring.
Educational demonstrations of radioactive decay.
Environmental monitoring (e.g., radon detection).

Carbon Dating (Radiocarbon Dating)

Radiocarbon dating exploits the predictable decay of carbon‑14 to estimate the age of organic materials.

Principle

Living organisms maintain a constant ratio of radioactive carbon‑14 (^{14}C) to stable carbon‑12 (^{12}C) through exchange with the atmosphere. Upon death, this exchange ceases, and the ^{14}C begins to decay while ^{12}C remains unchanged.

Decay of Carbon‑14

Carbon‑14 decays via beta emission with a half‑life of t_{1/2} = 5730 years:

^{14}C \rightarrow ^{14}N + e^- + \bar{\nu}_e

The decay constant is therefore:

\lambda = \frac{0.693}{5730\ \text{yr}} \approx 1.21 \times 10^{-4}\ \text{yr}^{-1}

Age Calculation

Measuring the current ^{14}C/^{12}C ratio (R) and comparing it to the modern atmospheric ratio (R_0) yields the sample age t:

t = -\frac{1}{\lambda} \ln\left(\frac{R}{R_0}\right)

Alternatively, using the half‑life form:

t = t_{1/2} \cdot \frac{\ln(R_0/R)}{\ln 2}

Example

A wooden artifact shows a ^{14}C/^{12}C ratio that is 0.35 of the modern value. Its age is:

t = -\frac{1}{1.21 \times 10^{-4}} \ln(0.35) \approx 8420\ \text{years}

Limitations

Effective for samples up to about 50 000 years (≈9 half‑lives); beyond this, remaining ^{14}C is too low for accurate measurement.
Requires calibration with tree‑ring data to account for historical variations in atmospheric ^{14}C production.
Contamination with modern carbon can skew results.

Medical Uses and Health Hazards of Radiation

Ionising radiation has transformative applications in medicine, but it also poses risks that must be managed through proper shielding, monitoring, and protocols.

Therapeutic Applications

Cancer Therapy (Radiotherapy): High‑energy gamma rays (from cobalt‑60 or linear accelerators) or beta particles destroy malignant cells by damaging their DNA. Techniques such as intensity‑modulated radiotherapy (IMRT) and gamma‑knife surgery allow precise targeting.
Brachytherapy: Sealed radioactive sources (e.g., iodine‑125, iridium‑192) are placed directly inside or near a tumour, delivering a localized dose.
Palliative Pain Relief: Radioisotopes like strontium‑89 are administered to alleviate bone pain from metastatic cancer.

Diagnostic Imaging

X‑ray Computed Tomography (CT): Uses rotating X‑ray beams to generate cross‑sectional images.
Nuclear Medicine: Gamma‑emitting tracers (e.g., technetium‑99m) are introduced into the body; a gamma camera detects emitted photons to visualise organ function (bone scans, cardiac perfusion).
Positron Emission Tomography (PET): Positron‑emitting isotopes (fluorine‑18) annihilate with electrons, producing coincident 511 keV gamma photons detected in a ring scanner.

Sterilisation

Gamma radiation from cobalt‑60 sources is employed to sterilise disposable medical equipment, pharmaceuticals, and tissue grafts, effectively killing microorganisms without leaving residues.

Health Hazards

Excessive or uncontrolled exposure to ionising radiation can cause deterministic and stochastic effects.

Radiation Sickness (Acute Radiation Syndrome): High doses (>1 Sv) produce nausea, vomiting, hematopoietic failure, and potentially death within days to weeks.
Cancer (Stochastic Effect): Even low doses increase the probability of inducing malignancies years after exposure; risk is considered linear with dose (no‑threshold model).
Genetic Damage: Radiation can cause mutations in germ cells, potentially affecting offspring.
Skin Burns and Cataracts: Localized high doses cause erythema, desquamation, and lens opacity.

Radiation Protection Principles

To minimise risk, the following principles are observed:

Justification: Any procedure involving radiation must yield a net benefit.
Optimization (ALARA): Doses should be kept As Low As Reasonably Achievable, using shielding, distance, and time reduction.
Dose Limits: Regulatory bodies set annual limits (e.g., 20 mSv for radiation workers, 1 mSv for the public).

“The beneficial uses of radiation in medicine far outweigh the risks when proper safety protocols are followed.” – International Commission on Radiological Protection (ICRP)

Summary

This chapter has detailed the fundamental characteristics of alpha, beta, and gamma radiation, presented the mathematical framework governing radioactive decay, and described practical detection and application techniques. From the Geiger‑Muller tube’s pulse‑counting mechanism to the archaeological power of carbon‑14 dating, and from life‑saving radiotherapy to the essential safeguards against radiation harm, the principles of radioactivity permeate both scientific inquiry and societal technology.

Unit 24: Radioactivity and Nuclear Reaction