Beta Decay
Beta decay is a type of radioactive decay mediated by the weak nuclear force, in which a neutron converts to a proton (beta-minus decay, emitting an electron and an antineutrino) or a proton converts to a neutron (beta-plus decay, emitting a positron and a neutrino). Unlike alpha decay, the mass number of the nucleus remains unchanged, but the atomic number increases or decreases by one. Beta decay is responsible for the natural transmutation of elements and is exploited in positron emission tomography (PET scanning) and food irradiation.
Key Formula
A_Z X → A_(Z+1) Y + e⁻ + antineutrino [β⁻ decay]
LaTeX: {}^{A}_{Z}X \rightarrow {}^{A}_{Z+1}Y + e^{-} + \bar{\nu}_e \quad (\beta^-)
| Symbol | Meaning | Unit |
|---|---|---|
| A | Mass number (unchanged) | dimensionless |
| Z | Atomic number of parent | dimensionless |
| e⁻ | Electron (beta particle) | — |
| ν̄ₑ | Electron antineutrino | — |
Worked Example
Problem
Carbon-14 (¹⁴₆C) undergoes beta-minus decay. Write the complete decay equation and identify the daughter nuclide.
Solution
Step 1: In β⁻ decay, a neutron → proton + electron + antineutrino. Step 2: Mass number is conserved: A_daughter = 14. Step 3: Atomic number increases by 1: Z_daughter = 6 + 1 = 7. Step 4: Element with Z = 7 is Nitrogen (N). Step 5: Write: ¹⁴₆C → ¹⁴₇N + e⁻ + ν̄ₑ.
Answer
The daughter nuclide is Nitrogen-14 (¹⁴₇N).
Comparison of Beta-Minus and Beta-Plus Decay
| Property | Beta-Minus (β⁻) | Beta-Plus (β⁺) | Electron Capture |
|---|---|---|---|
| Nuclear change | n → p | p → n | p + e⁻ → n |
| Particle emitted | Electron (e⁻) | Positron (e⁺) | Neutrino (νₑ) |
| Lepton emitted | Antineutrino (ν̄ₑ) | Neutrino (νₑ) | Neutrino (νₑ) |
| Atomic number change | +1 | −1 | −1 |
| Example | C-14 → N-14 | Na-22 → Ne-22 | Fe-55 → Mn-55 |
| Medical use | Radiation therapy | PET scanning | Diagnostics |
Interactive Tools
PhET Nuclear Decay Simulator
Interactive beta decay simulations with visual nuclear transformation
Open ToolKhan Academy: Beta Decay
Detailed explanation of beta-minus, beta-plus, and electron capture
Open ToolWolfram Alpha Nuclear Calculator
Look up decay equations and nuclear properties for any isotope
Open Tool
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Related Terms
Radioactive Decay
Radioactive decay is the spontaneous transformation of an unstable atomic nucleus into a more stable configuration by emitting radiation in the form of particles or electromagnetic waves. This process occurs because the nucleus has too many protons, too many neutrons, or excess energy, making it thermodynamically unstable. It is the foundation of nuclear medicine, radiometric dating, and nuclear power generation.
Alpha Decay
Alpha decay is a type of radioactive decay in which an unstable nucleus emits an alpha particle — a helium-4 nucleus consisting of two protons and two neutrons — thereby reducing its atomic number by 2 and its mass number by 4. This process is common in heavy nuclei (Z > 82) such as uranium and radium, where the nuclear repulsion between protons becomes too great to maintain stability. Alpha particles have low penetrating power and can be stopped by a sheet of paper, but are highly ionising and dangerous if ingested or inhaled.
Gamma Radiation
Gamma radiation consists of high-energy electromagnetic photons emitted by an excited atomic nucleus as it transitions from a higher energy state to a lower one, typically following alpha or beta decay. Unlike alpha and beta radiation, gamma rays carry no charge and no mass, so gamma emission does not change the atomic number or mass number of the nucleus. Due to their extremely high energy (typically 10 keV to 10 MeV) and penetrating power, gamma rays are used in cancer radiotherapy, sterilisation of medical equipment, and industrial non-destructive testing.
Named "beta" by Ernest Rutherford in 1899 using the second letter of the Greek alphabet (β), distinguishing it from alpha radiation by its greater penetrating power. The underlying mechanism involving the weak force was not understood until Enrico Fermi's theory of beta decay in 1934.