Nuclear Chemistry

Overview of Nuclear Chemistry

Nuclear chemistry deals with changes in the atomic nucleus and their chemical consequences. Unlike “ordinary” chemical reactions, which involve electrons and chemical bonds, nuclear processes involve transformations of protons and neutrons inside the nucleus. These processes can change one element into another and release or absorb very large amounts of energy.

In this chapter, the focus is on what is characteristic of nuclear processes as opposed to chemical ones, on the ways we describe them, and on their main types and applications. The structure of nuclei, their detailed stability, and the cosmic origin of elements are treated in the following chapters.

Nuclear vs. Chemical Reactions

Chemical reactions:

• Involve rearrangement of electrons and chemical bonds.
• Do not change the atomic nuclei; the elements themselves remain the same.
• Energies involved are typically on the order of a few hundred kJ per mole.

Nuclear reactions:

• Involve changes in the composition or energy state of nuclei.
• Can transform one element into another (nuclear transmutation).
• Energies involved are much larger, often millions of times greater per event than typical bond energies.

Key distinctions:

• Electron involvement: Chemical reactions involve valence electrons; nuclear reactions involve nucleons (protons and neutrons).
• Isotope sensitivity: Reaction rates in chemistry depend strongly on temperature, concentration, catalysts, etc., and only slightly on isotope (with some kinetic isotope effects). Nuclear decay rates are largely independent of chemical environment, temperature, and pressure.
• Mass–energy relation: In nuclear processes, small mass differences are converted into large amounts of energy according to $E = mc^2$.

Basic Terminology and Notation

Nuclear Symbols

Nuclei are described with nuclide symbols of the form
$$
{}^{A}_{Z}\text{X}
$$
where:

• $X$ is the chemical symbol of the element.
• $Z$ is the atomic number (number of protons).
• $A$ is the mass number (total number of protons and neutrons).

The number of neutrons is $N = A - Z$.

Examples:

• $^{1}_{1}\text{H}$: ordinary hydrogen (1 proton, 0 neutrons).
• $^{4}_{2}\text{He}$: helium-4 (2 protons, 2 neutrons).
• $^{14}_{6}\text{C}$: carbon-14 (6 protons, 8 neutrons).

Nuclei with the same $Z$ but different $A$ are isotopes of the same element.

Types of Nuclear Particles and Radiation

Common particles and forms of radiation encountered in nuclear chemistry include:

• Alpha particle: $^4_2\text{He}$ nucleus, often written $\alpha$.
• Beta particle:
• $\beta^-$: electron emitted from the nucleus.
• $\beta^+$: positron (positively charged electron).
• Gamma radiation ($\gamma$): high-energy electromagnetic radiation emitted from an excited nucleus.
• Neutron: $^1_0\text{n}$, electrically neutral nucleon.
• Proton: $^1_1\text{H}$ or $^1_1\text{p}$, positively charged nucleon.
• Neutrino / antineutrino ($\nu$, $\bar\nu$): very light, neutral particles involved in beta processes; important for completeness but often omitted in simplified balances.

In nuclear equations, these species are treated like “reactants” and “products,” and conservation laws must be respected.

Conservation Laws in Nuclear Processes

Every nuclear reaction or decay obeys several conservation principles:

• Conservation of nucleon number: The sum of mass numbers $A$ of all reactants equals the sum of $A$ of all products.
• Conservation of charge (atomic number): The sum of atomic numbers $Z$ of reactants equals the sum of $Z$ of products.
• Conservation of energy: Total energy, including rest mass energy, is conserved.
• Conservation of momentum and other quantities (such as lepton number) are also obeyed, though often not treated in detail at the introductory level.

Example of a balanced nuclear equation:
$$
{}^{238}_{92}\text{U} \rightarrow {}^{234}_{90}\text{Th} + {}^{4}_{2}\text{He}
$$
Check:

• Mass numbers: $238 = 234 + 4$
• Atomic numbers: $92 = 90 + 2$

Radioactive Decay

Radioactive decay is a spontaneous nuclear process in which an unstable nucleus transforms into a more stable one, emitting radiation. It is characterized by:

• Occurring without external influence (not triggered by temperature, pressure, etc.).
• Having a probabilistic nature: each nucleus has a certain probability per unit time to decay.
• Being described statistically for large numbers of nuclei (half-life, decay constant).

Types of Radioactive Decay

Only the character of the most common modes is outlined here; their role in nuclear stability is further developed elsewhere.

Alpha Decay ($\alpha$)

In alpha decay, the nucleus emits an alpha particle (${}^{4}_{2}\text{He}$), reducing both its mass and atomic numbers:
$$
{}^{A}_{Z}\text{X} \rightarrow {}^{A-4}_{Z-2}\text{Y} + {}^{4}_{2}\text{He}
$$

Example:
$$
{}^{238}_{92}\text{U} \rightarrow {}^{234}_{90}\text{Th} + {}^{4}_{2}\text{He}
$$

Alpha decay is typical for heavy nuclei.

Beta Minus Decay ($\beta^-$)

In beta minus decay, a neutron in the nucleus transforms into a proton, emitting an electron ($\beta^-$) and an antineutrino ($\bar\nu_e$):
$$
\text{n} \rightarrow \text{p} + \beta^- + \bar\nu_e
$$

At the nuclear level:
$$
{}^{A}_{Z}\text{X} \rightarrow {}^{A}_{Z+1}\text{Y} + \beta^- + \bar\nu_e
$$

Example:
$$
{}^{14}_{6}\text{C} \rightarrow {}^{14}_{7}\text{N} + \beta^- + \bar\nu_e
$$

$A$ remains constant, $Z$ increases by 1.

Beta Plus Decay ($\beta^+$) and Electron Capture

In beta plus decay, a proton transforms into a neutron, emitting a positron ($\beta^+$) and a neutrino:
$$
\text{p} \rightarrow \text{n} + \beta^+ + \nu_e
$$

Nuclear form:
$$
{}^{A}_{Z}\text{X} \rightarrow {}^{A}_{Z-1}\text{Y} + \beta^+ + \nu_e
$$

Alternatively, in electron capture, the nucleus captures an inner-shell electron, turning a proton into a neutron and emitting a neutrino:
$$
{}^{A}_{Z}\text{X} + e^- \rightarrow {}^{A}_{Z-1}\text{Y} + \nu_e
$$

Both processes effectively reduce $Z$ by 1 while leaving $A$ unchanged.

Gamma Emission ($\gamma$)

After a nuclear transformation, the resulting nucleus may be in an excited energy state. It can relax to a lower-energy state by emitting a gamma photon:
$$
{}^{A}_{Z}\text{X}^* \rightarrow {}^{A}_{Z}\text{X} + \gamma
$$
No change in $A$ or $Z$, only in nuclear energy.

Half-Life and Radioactive Decay Law

Half-life ($t_{1/2}$) is the time required for half of the nuclei in a radioactive sample to decay. It is a characteristic constant for each radionuclide.

The number of undecayed nuclei $N$ at time $t$ is given by:
$$
N(t) = N_0 e^{-\lambda t}
$$
where:

• $N_0$ is the initial number of nuclei at $t = 0$.
• $\lambda$ is the decay constant (probability per unit time that a nucleus decays).

The half-life is related to $\lambda$ by:
$$
t_{1/2} = \frac{\ln 2}{\lambda}
$$

The activity $A$ of a sample (number of decays per unit time) is:
$$
A = \lambda N
$$
Activity is measured in becquerels (Bq), where $1\ \text{Bq} = 1$ decay per second.

Nuclear Reactions

Besides spontaneous decay, nuclei can undergo reactions when bombarded with particles such as neutrons, protons, alpha particles, or other nuclei.

A general nuclear reaction can be written as:
$$
\text{Target} + \text{Projectile} \rightarrow \text{Products}
$$

Example:
$$
{}^{14}_{7}\text{N} + {}^{1}_{0}\text{n} \rightarrow {}^{14}_{6}\text{C} + {}^{1}_{1}\text{H}
$$

Again, $A$ and $Z$ are conserved across the equation.

Types of Nuclear Reactions (Overview)

Only the basic character of these reactions is outlined here; their energetic and stability aspects are developed in more detail in subsequent sections.

• Neutron capture: Nucleus absorbs a neutron; may lead to a heavier isotope and often to subsequent decay:
  $$
  {}^{A}_{Z}\text{X} + {}^{1}_{0}\text{n} \rightarrow {}^{A+1}_{Z}\text{X}^{*} \rightarrow \dots
  $$
• Particle emission reactions: Emission of neutrons, protons, or alpha particles after being excited.
• Induced transmutation: Bombardment of elements with particles (e.g., in accelerators or reactors) to create new elements or isotopes.
• Fission: Splitting of a heavy nucleus into two (or more) lighter nuclei plus neutrons and energy.
• Fusion: Combination of light nuclei to form a heavier nucleus, releasing energy.

The nuclear stability considerations that influence which reactions are possible or favorable are handled separately in the chapter on nuclear stability and reactions.

Mass Defect and Binding Energy

Nuclei have a binding energy, the energy required to completely separate a nucleus into its individual protons and neutrons. Because of $E = mc^2$, this binding energy is reflected in a mass defect: the mass of a nucleus is less than the sum of the masses of its free nucleons.

For a nucleus with $Z$ protons and $N$ neutrons:

• Sum of separate nucleon masses:
  $$
  m_{\text{nucleons}} = Z m_{\text{p}} + N m_{\text{n}}
  $$
• Measured nuclear mass: $m_{\text{nucleus}}$
• Mass defect:
  $$
  \Delta m = m_{\text{nucleons}} - m_{\text{nucleus}}
  $$
• Binding energy:
  $$
  E_\text{B} = \Delta m\, c^2
  $$

The binding energy per nucleon is an important quantity for understanding why some nuclear processes release energy and others require it. Details of how binding energy varies across the periodic table and drives fission and fusion are taken up in later sections.

Nuclear Fission and Fusion (Introductory View)

Nuclear Fission

In nuclear fission, a heavy nucleus (such as uranium-235) splits into two medium-mass nuclei, along with several neutrons and a large energy release.

Example (simplified):
$$
{}^{235}_{92}\text{U} + {}^{1}_{0}\text{n} \rightarrow {}^{141}_{56}\text{Ba} + {}^{92}_{36}\text{Kr} + 3\,{}^{1}_{0}\text{n} + \text{energy}
$$

Key points:

• Triggered by neutron absorption.
• Can lead to a chain reaction because released neutrons can induce further fissions.
• Basis of nuclear reactors and nuclear weapons.

The criticality conditions and technical implementation are topics of application-oriented discussions rather than core nuclear chemistry concepts.

Nuclear Fusion

Nuclear fusion combines light nuclei (e.g., isotopes of hydrogen) into heavier ones, releasing energy.

Example:
$$
{}^{2}_{1}\text{H} + {}^{3}_{1}\text{H} \rightarrow {}^{4}_{2}\text{He} + {}^{1}_{0}\text{n} + \text{energy}
$$

Fusion:

• Requires extremely high temperatures and pressures to overcome electrostatic repulsion between positively charged nuclei.
• Powers stars, including the Sun.
• Is central to the cosmic synthesis of elements, treated further in the nuclear synthesis chapters.

Detection and Measurement of Nuclear Radiation

Nuclear chemistry uses several techniques to detect and quantify nuclear radiation, enabling both fundamental studies and practical applications.

Common principles (without device-specific engineering detail):

• Ionization of matter: Many detectors (ionization chambers, Geiger–Müller tubes) rely on the fact that ionizing radiation produces ion pairs in gases or solids, leading to detectable electrical signals.
• Scintillation: Some materials emit light (scintillate) when radiation deposits energy in them; the light is detected by photomultipliers or photodiodes.
• Solid-state detectors: Semiconductor materials produce electron–hole pairs when interacting with radiation; the resulting currents are measurable.

Quantities used:

• Activity (Bq): number of decays per second.
• Absorbed dose: energy deposited per unit mass (gray, Gy).
• Dose equivalent / effective dose: accounts for biological effect (sievert, Sv), combining dose with radiation type and tissue weighting.

Detailed dosimetry and biological effects are typically covered where radiation safety or applications are emphasized.

Applications of Nuclear Chemistry

Nuclear chemistry underlies many modern technologies and scientific methods. Only the nuclear-chemical aspects are highlighted here; broader context is treated in application chapters.

Radiometric Dating

Radiometric dating uses the known half-lives of radioactive isotopes to determine the age of materials.

Basic idea:

• Measure the ratio of parent radionuclide to its decay product.
• Use the decay law to calculate the time elapsed.

Example: Carbon-14 dating for formerly living materials using the $^{14}\text{C}/^{12}\text{C}$ ratio.

Tracer Techniques

Radioisotopes can be used as tracers:

• A radioactively labeled form of a compound is introduced into a system.
• Its movement, reaction pathway, or distribution is followed by detecting emitted radiation.
• Widely used in chemistry, biology, medicine, and environmental studies.

Key nuclear-chemical aspect: choice of radionuclide with suitable half-life, radiation type, and chemical behavior (must mimic the stable isotope).

Nuclear Medicine

Nuclear chemistry concepts are essential for:

• Diagnostic imaging: e.g., positron emission tomography (PET) uses positron-emitting radionuclides; single-photon emission computed tomography (SPECT) uses gamma emitters.
• Radiotherapy: Controlled application of ionizing radiation to destroy cancer cells.

Important nuclear aspects include decay modes, energies of emitted radiation, and half-lives to balance imaging efficacy, patient dose, and logistics.

Power Generation and Industrial Uses

• Nuclear reactors: Use controlled fission chain reactions to generate heat, converted to electricity.
• Industrial radiography: Radiation sources used to inspect materials (e.g., weld integrity) non-destructively.
• Sterilization and preservation: Ionizing radiation used to sterilize medical equipment or food.

In all such applications, nuclear chemistry provides the understanding necessary to select appropriate isotopes, manage decay, and handle radioactive materials safely.

Safety and Handling of Radioactive Materials

Working with radioactive substances requires an understanding of basic protection principles derived from nuclear chemistry:

• Time: Minimize time of exposure.
• Distance: Maximize distance from sources (intensity decreases with distance).
• Shielding: Use materials that effectively absorb or attenuate different radiation types:
• $\alpha$: stopped by paper or skin but hazardous if ingested or inhaled.
• $\beta$: requires light shielding (plastic, aluminum).
• $\gamma$ and high-energy X-rays: require dense shielding (lead, concrete).

Nuclear chemistry also underpins:

• Concepts of contamination vs. irradiation.
• Strategies for waste management (e.g., based on half-lives and decay products).
• Monitoring of radiation levels and environmental pathways of radionuclides.

These topics bridge into environmental and applied chemistry chapters where broader context is given.

Summary of Key Ideas

• Nuclear chemistry focuses on changes in atomic nuclei, distinct from chemical reactions involving electrons.
• Nuclear processes obey conservation of nucleon number, charge, and energy; these are applied to balance nuclear equations.
• Radioactive decay is spontaneous and statistical, characterized by decay constants and half-lives.
• Nuclear reactions include decay processes, particle-induced transformations, fission, and fusion.
• Mass defects correspond to nuclear binding energies; they explain the enormous energy changes in nuclear processes.
• Detection, measurement, and applications of nuclear radiation rely on nuclear-chemical principles and are central to dating, tracing, medicine, power generation, and industry.