1.1 Defining Radioactive Decay

Radioactive decay is a natural and irreversible process at the heart of nuclear physics. It is defined as the spontaneous transformation of an unstable atomic nucleus into a more stable, energetically favourable one through the emission of radiation.[^1] This process is driven by the nucleus's inherent instability, which is caused by an imbalance in the number of protons and neutrons or an excess of internal energy.[^4]

To fully grasp this concept, one can envision an unstable nucleus as a precarious, "shaky stack of building blocks".[^7] While it may appear stable for a time, its internal configuration is unstable, and pieces will eventually "fall off" as it releases excess energy to find a more balanced and secure structure.[^7] This emission of particles or energy is precisely what constitutes radioactive decay, leading to a new nucleus that is more stable.[^5]

1.2 The Spontaneous and Random Nature of Decay

A critical aspect of radioactive decay is its dual nature: it is both spontaneous and random. These two characteristics are often conflated but describe distinct yet interconnected properties of the decay process.

• Spontaneous signifies that radioactive decay occurs entirely on its own, without any external influence or trigger.[^1] It is a self-initiated nuclear event, meaning it is not affected by external factors such as changes in temperature, pressure, or the nucleus's chemical environment.[^2]
• Random refers to the unpredictability of the decay event.[^1] It is impossible to predict precisely which individual nucleus in a sample will decay or at what exact moment it will transform.[^1] This unpredictability is a direct consequence of the spontaneous nature of decay. The process is governed by chance, which is why scientists rely on probability and statistical measures like half-life to predict the behaviour of large populations of nuclei rather than the fate of a single atom.[^7]

2.1 The Concept of Nuclear Stability

Nuclear stability is a delicate balance of forces within the atomic nucleus.[^4] The nucleus is composed of protons and neutrons, collectively known as nucleons.[^5] Two primary forces are at play: the strong nuclear force, which is an attractive force that holds the nucleons together, and the electrostatic force, which is a repulsive force between the positively charged protons.[^10] For a nucleus to be stable, these forces must be in a state of equilibrium.[^4]

A nucleus becomes unstable, and thus radioactive, when this balance is disrupted. This typically occurs for three main reasons: an excess of neutrons, an excess of protons, or a nucleus that is simply too large.[^4] To correct this imbalance and release the excess internal energy, the nucleus undergoes radioactive decay.[^3]

2.2 The "Band of Stability"

The relationship between the number of neutrons and protons that leads to a stable nucleus can be visualised on a plot of neutron number (N) against proton number (Z), often called the "Band of Stability".[^11]

For lighter elements, stability is achieved when the neutron-to-proton ratio is approximately 1:1. As the atomic number (Z) increases, however, the electrostatic repulsion between the growing number of protons becomes more significant.[^11] Consequently, for very heavy elements, the stable neutron-to-proton ratio increases to about 1.5:1.[^13]

A nucleus's position relative to this band provides a powerful predictive tool for the type of decay it will undergo. A nucleus with an excess of neutrons will lie above the band of stability and typically undergoes beta decay. Conversely, a nucleus that is too heavy (atomic number > 83) lies at the upper right and will likely undergo alpha decay.[^6]

Radioactive decay can result in the emission of three primary types of radiation: alpha particles, beta particles, and gamma rays. Each type has a unique composition and distinct physical properties.

3.1 Alpha (α) Radiation

Alpha particles (α) are composite particles consisting of two protons and two neutrons, making them identical to a helium nucleus.[^3] They are the heaviest and slowest of the three primary types of radiation, with a relative mass of 4 a.m.u. and a positive charge of +2e.[^3]

Because of their large size and high charge, alpha particles have a strong ionising effect but are weakly penetrating.[^1] They can be stopped completely by a single sheet of paper or human skin.[^7]

Safety Note: As an external source, alpha particles pose minimal risk. However, if an alpha-emitting material is ingested or inhaled, it becomes extremely dangerous due to the intense damage to internal tissues.[^7]

3.2 Beta (β) Radiation

Beta particles (β) are high-speed electrons emitted from an unstable nucleus.[^7] A neutron within the nucleus transforms into a proton, and the electron is ejected.[^1]

Beta particles have a negligible mass and a negative charge of -1e.[^10] They have a greater penetrating ability than alpha particles (stopped by thin aluminium) and a moderate ionising effect.[^17]

3.3 Gamma (γ) Radiation

Gamma rays (γ) are not particles but are a form of high-energy electromagnetic radiation.[^3] They have no mass and no charge.[^3]

Gamma emission typically occurs after a nucleus has undergone a previous alpha or beta decay, releasing excess energy.[^10] Due to having no charge or mass, gamma rays are highly penetrating (requiring thick lead or concrete to shield) and are the least ionising of the three types.[^17]

3.4 Comparative Analysis of Radiation Types

Nuclear equations represent the transformations during radioactive decay, conserving both mass (nucleon) number and atomic (proton) number.[^10]

4.1 Writing Alpha Decay Equations

Alpha decay involves the emission of a helium nucleus ($^{4}_{2}$He). The parent nucleus loses 2 protons and 2 neutrons, so the atomic number (Z) decreases by 2, and the mass number (A) decreases by 4.[^6]

Example: Uranium-238 decay

4.2 Writing Beta Decay Equations

Beta decay involves a neutron transforming into a proton, emitting an electron ($^{0}_{-1}$e). The mass number (A) is unchanged, but the atomic number (Z) increases by 1.[^6]

Example: Carbon-14 decay

4.3 Writing Gamma Decay Equations

Gamma decay involves the emission of a gamma ray photon (γ) from an excited nucleus (denoted by *). The composition, mass number, and atomic number remain unchanged.[^6]

Example: Barium-137m decay

5.1 Definition and Significance

Half-life is the time it takes for half of the unstable nuclei in a given sample to decay, or for the activity of the sample to fall to half its initial value.[^1] It is a constant value for a specific radioactive isotope.[^7]

5.2 Half-Life Calculations and Graphs

Half-life follows an exponential decay pattern.

Important Note: When measuring activity, it is essential to first measure the background radiation and subtract it from all readings to get the corrected count rate of the source alone.[^34]

6.1 What is Background Radiation?

Background radiation is the weak, naturally occurring ionising radiation that is present in the environment all around us.[^1]

6.2 Sources of Background Radiation

• Natural Sources:
• Radon Gas: From the decay of uranium in rocks and soil.[^1]
• Cosmic Rays: High-energy particles from space.[^1]
• Rocks and Buildings: Natural radioactivity in building materials.[^3]
• Food and Drink: Small amounts of radioactive elements like potassium-40.[^39]
• Man-Made Sources:
• Medical Procedures: X-rays, CT scans, and radiation therapy.[^23]
• Nuclear Fallout: From past nuclear weapons testing and accidents.[^23]

6.3 Corrected Count Rate

In laboratory experiments, the corrected count rate is found by:

Corrected Count Rate = Total Count Rate - Background Count Rate

This procedure is crucial for accurate measurements of a source's activity.[^34]

7.1 Summary of Key Concepts

Radioactive decay is a spontaneous and random nuclear process where unstable nuclei emit alpha, beta, or gamma radiation to achieve stability. The properties of these emissions are directly linked, and their decay rate is quantified by half-life.

7.2 Dangers and Safety Precautions

Ionising radiation can damage living cells and DNA, potentially leading to cancer.[^1] Key safety protocols are:

1. Minimising time of exposure.
2. Maximising distance from the source.
3. Using appropriate shielding (paper for α, aluminium for β, lead/concrete for γ).

7.3 Practical Applications of Radioactivity

• Medicine: Gamma-emitting tracers for imaging (e.g., technetium-99m) and radiotherapy for cancer treatment.[^23]
• Industry: Beta-emitters for thickness monitoring of materials.[^23]
• Home: Alpha-emitters in smoke detectors.[^23]