Nuclear Decay Modes & Equations

Alpha decay occurs when a heavy nucleus emits an alpha particle, which is identical to a helium-4 nucleus: two protons and two neutrons tightly bound together, written as $^{4}_{2}\text{He}$. Because the parent nucleus loses 2 protons and 2 neutrons, the mass number A decreases by 4 and the atomic number Z decreases by 2. Alpha decay is most common in very heavy nuclei (Z > 83) where the nucleus is too large to remain stable. Alpha particles are the least penetrating form of radiation — they can be stopped by a sheet of paper or a few centimetres of air — but they are highly ionizing and very dangerous if inhaled or ingested. A classic example is the alpha decay of uranium-238: $\ce{^{238}_{92}U -> ^{234}_{90}Th + ^{4}_{2}He}$.

Beta decay comes in two types. In beta-minus (β⁻) decay, a neutron in the nucleus converts into a proton, releasing a high-energy electron (the beta particle, $^{0}_{-1}e$) and an antineutrino. This increases Z by 1 while A remains unchanged: $\ce{^{A}_{Z}X -> ^{A}_{Z+1}Y + ^{0}_{-1}e + \bar{\nu}_e}$. β⁻ decay happens when a nucleus has too many neutrons relative to protons. In beta-plus (β⁺) decay, a proton converts into a neutron, emitting a positron ($^{0}_{+1}e$) and a neutrino. This decreases Z by 1 while A stays the same, and occurs when a nucleus has too many protons. A common example of β⁻ decay is carbon-14: $\ce{^{14}_{6}C -> ^{14}_{7}N + ^{0}_{-1}e}$. Beta particles are more penetrating than alpha particles but can be stopped by a few millimetres of aluminium.

Gamma decay involves the emission of a high-energy photon (gamma ray, $^{0}_{0}\gamma$) from an excited nucleus. Unlike alpha and beta decay, gamma emission does NOT change the atomic number or mass number — it only releases excess energy. Gamma decay almost always accompanies alpha or beta decay, since the daughter nucleus is often left in an excited (high-energy) state. Gamma rays are electromagnetic radiation with very short wavelengths and are the most penetrating form of nuclear radiation, requiring centimetres of lead or metres of concrete to be effectively shielded. The notation $^{A}_{Z}X^*$ is used to denote an excited nuclear state (nuclear isomer).

Nuclear equations must satisfy two conservation laws: (1) Conservation of mass number — the sum of all mass numbers (A) on the left must equal the sum on the right. (2) Conservation of atomic number (charge) — the sum of all atomic numbers (Z) on the left must equal the sum on the right. To balance a nuclear equation, identify the unknown particle by subtracting the known A and Z values. For example, if radon-222 undergoes alpha decay: $\ce{^{222}_{86}Rn -> ^{A}_{Z}X + ^{4}_{2}He}$. Conservation gives A = 222 − 4 = 218 and Z = 86 − 2 = 84, so the daughter nucleus is $\ce{^{218}_{84}Po}$ (polonium-218).

• A — Mass Number (dimensionless): Total number of protons and neutrons (nucleons) in the nucleus. Conserved on both sides of the equation.
• Z — Atomic Number (dimensionless): Number of protons in the nucleus. Determines the element identity. Conserved on both sides of the equation.
• ^{4}_{2}\text{He} — Alpha Particle (dimensionless): The alpha particle: a helium-4 nucleus consisting of 2 protons and 2 neutrons, emitted with high kinetic energy during alpha decay.
• ^{0}_{-1}e — Beta Particle (electron) (dimensionless): A high-speed electron emitted from the nucleus during beta-minus decay, carrying away energy along with an antineutrino.
• ^{0}_{0}\gamma — Gamma Ray (dimensionless): A high-energy photon emitted when an excited daughter nucleus relaxes to its ground state. Carries no mass or charge.

Problem. Thorium-234 undergoes beta-minus decay. Write the balanced nuclear equation and identify the daughter nucleus.

Answer. The daughter nucleus is Protactinium-234 (Pa-234). The beta particle carries away energy and an antineutrino is also released.

• Radioactive Half-Life and Decay Rates — Half-life quantifies how quickly a radioactive nucleus decays over time, extending the concept of nuclear decay modes into kinetics and practical applications like carbon-14 dating.
• Nuclear Binding Energy and Mass Defect — The energy released in nuclear decay is explained by the mass defect — the difference between nuclear mass and the sum of its nucleon masses — using Einstein's E = mc² relationship.
• Isotopes and Atomic Mass — Nuclear decay modes change the number of protons or neutrons, directly converting one isotope or element into another, making isotope concepts foundational to understanding decay.
• Nuclear Fission and Fusion — Fission and fusion are large-scale nuclear reactions that, like decay, involve changes to the nucleus and the release of enormous amounts of energy, and are governed by the same conservation laws.