9.3 Radioactivity and Decay Processes

Radioactivity is the spontaneous emission of radiation from unstable atomic nuclei. It's a natural process that transforms one element into another, discovered by Henri Becquerel in 1896 while studying uranium salts.

This section explores the types of radioactive decay: alpha, beta, and gamma. We'll learn about their characteristics, how to balance nuclear equations, and the concept of decay series. Understanding these processes is crucial for nuclear physics applications.

Radioactivity and its origins

Discovery and fundamental concepts

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• Radioactivity describes spontaneous emission of radiation from unstable atomic nuclei transforming one element into another
• Henri Becquerel discovered radioactivity in 1896 while studying uranium salts
• Marie and Pierre Curie conducted further investigations expanding knowledge of radioactive elements
• Natural radioactivity occurs in elements with atomic numbers greater than 83 (uranium, thorium, radium)
• Artificial radioactivity induced in stable nuclei through nuclear reactions (technetium-99m, cobalt-60)

Causes and characteristics of radioactivity

• Instability in radioactive nuclei arises from imbalance in proton-neutron ratio or excess nuclear energy
• Half-life characterizes rate of radioactive decay unique to each radioisotope
• Half-life remains independent of external factors (temperature, pressure)
• Radioactive decay follows first-order kinetics decay rate proportional to number of radioactive nuclei present
• Decay constant (λ) relates to half-life through equation: $t_{1/2} = \frac{\ln(2)}{\lambda}$

Types of radioactive decay

Alpha decay

• Emission of alpha particle (two protons and two neutrons) from parent nucleus
• Reduces atomic number by 2 and mass number by 4
• Alpha particles highly ionizing but least penetrating (stopped by sheet of paper)
• Energy spectrum discrete peaks due to quantized nuclear energy levels
• Example decay equation: $_{88}^{226}Ra \rightarrow _{86}^{222}Rn + _{2}^{4}He$

Beta decay

• Three forms beta-minus (β⁻), beta-plus (β⁺), and electron capture
• β⁻ decay emits electron and antineutrino (neutron converts to proton)
• β⁺ decay emits positron and neutrino (proton converts to neutron)
• Electron capture inner orbital electron captured by nucleus converting proton to neutron
• Beta particles moderately ionizing and penetrating (stopped by thin aluminum sheet)
• Energy spectrum continuous due to energy sharing between emitted particles
• Example β⁻ decay: $_{6}^{14}C \rightarrow _{7}^{14}N + _{-1}^{0}e + \bar{\nu}_{e}$

Gamma decay

• Emission of high-energy photons (gamma rays) from excited nucleus
• No change in atomic number or mass number
• Gamma rays least ionizing but most penetrating (requires thick lead shielding)
• Energy spectrum discrete peaks corresponding to nuclear energy level transitions
• Often accompanies alpha or beta decay as nucleus de-excites
• Example gamma decay: $_{27}^{60}Co^* \rightarrow _{27}^{60}Co + \gamma$

Balancing nuclear decay equations

General principles

• Nuclear decay equations must balance atomic number (Z) and mass number (A) on both sides
• Conservation of electric charge and nucleon number fundamental to balancing equations
• Use correct superscript and subscript notation for each particle (mass number top, atomic number bottom)
• Account for all emitted particles including neutrinos and antineutrinos in beta decay

Specific decay equations

• Alpha decay equation: $_{Z}^{A}X \rightarrow _{Z-2}^{A-4}Y + _{2}^{4}He$
• Beta-minus decay equation: $_{Z}^{A}X \rightarrow _{Z+1}^{A}Y + _{-1}^{0}e + \bar{\nu}$
• Beta-plus decay equation: $_{Z}^{A}X \rightarrow _{Z-1}^{A}Y + _{+1}^{0}e + \nu$
• Electron capture equation: $_{Z}^{A}X + _{-1}^{0}e \rightarrow _{Z-1}^{A}Y + \nu$
• Gamma decay equation: $_{Z}^{A}X^* \rightarrow _{Z}^{A}X + \gamma$

Decay series and daughter nuclides

Decay series concepts

• Decay series describes sequence of radioactive decays from parent nuclide to stable daughter nuclide
• Common naturally occurring decay series uranium series, thorium series, actinium series
• Each series starts with long-lived parent nuclide ends with stable isotope of lead
• Branching decay occurs when parent nuclide decays via multiple modes with specific branching ratios
• Example uranium-238 decay series involves 14 steps before reaching stable lead-206

Daughter nuclides and equilibrium

• Daughter nuclides products of radioactive decay may be radioactive or stable isotopes
• Secular equilibrium arises when parent nuclide half-life much longer than daughter nuclides
• In secular equilibrium ratio of parent to daughter nuclides remains constant over time
• Equation for secular equilibrium: $\lambda_1 N_1 = \lambda_2 N_2$
• Where λ₁, N₁ are decay constant and number of atoms of parent, λ₂, N₂ for daughter

Applications of decay series

• Radiometric dating determines age of geological samples (carbon-14 dating, uranium-lead dating)
• Nuclear forensics analyzes radioactive materials to determine origin and history
• Understanding behavior of naturally occurring radioactive materials (NORM) in environment
• Radon gas mitigation in buildings based on understanding uranium decay series
• Radioactive tracers in medical imaging (technetium-99m from molybdenum-99 decay)