Beta particle
A beta particle, also known as a beta ray when referring to the radiation stream, is a high-energy, high-speed electron or positron emitted from the nucleus of a radioactive atom during beta decay.[1] These particles arise when an unstable nucleus seeks greater stability by adjusting its neutron-to-proton ratio, with electrons (beta-minus particles) emitted in beta-minus decay and positrons (beta-plus particles) in beta-plus decay.[2] Beta particles typically carry kinetic energies ranging from a few kiloelectronvolts to several megaelectronvolts, enabling them to ionize atoms along their path but with penetrating power intermediate between alpha particles and gamma rays—they can travel several meters in air but are stopped by a few millimeters of plastic or light metal shielding.[3][4] Beta decay occurs in approximately 97% of known unstable isotopes and involves the weak nuclear force, transforming a neutron into a proton (or vice versa) while conserving charge and lepton number through the emission of a neutrino or antineutrino.[1] In beta-minus decay, a neutron decays into a proton, electron, and antineutrino, increasing the atomic number by one without changing the mass number.[5] Conversely, beta-plus decay converts a proton into a neutron, positron, and neutrino, decreasing the atomic number by one.[1] This process was first observed in 1896 by Henri Becquerel during his studies of uranium salts, which revealed penetrating rays beyond X-rays, and was further characterized in 1899 by Ernest Rutherford, who identified beta rays as streams of high-velocity electrons deflected by magnetic fields.[6][7] Beta particles play a crucial role in both natural processes and human applications, contributing to phenomena like cosmic ray interactions and stellar nucleosynthesis while posing health risks through ionization that can damage DNA if internalized.[2] In medicine, beta emitters are harnessed for radiotherapy to target cancer cells, such as in radioimmunotherapy, and for diagnostics via positron emission tomography (PET) scans using beta-plus decay.[8] Industrially, they enable non-destructive testing, including thickness gauging of materials in manufacturing and leak detection in pipelines.[4] Ongoing research explores beta decay for neutrino studies, advancing particle physics understanding of the weak interaction.[9]Fundamentals
Definition and Types
A beta particle is a high-energy, charged particle emitted from the nucleus of a radioactive atom during beta decay, serving as a form of ionizing radiation that differs from alpha particles (helium nuclei) and gamma rays (high-energy photons). These particles originate from instabilities in the atomic nucleus, where an imbalance in the proton-to-neutron ratio prompts emission to achieve greater stability.[10][1][2] There are two main types of beta particles, both mediated by the weak nuclear force: beta-minus (β⁻) particles, which are electrons released when a neutron decays into a proton, and beta-plus (β⁺) particles, which are positrons emitted when a proton decays into a neutron. This process allows the nucleus to adjust its composition without altering the total number of nucleons.[11][10][3] Beta particles possess a rest mass of approximately 0.511 MeV/c², equivalent for both electrons and positrons, and their velocities can range from near zero up to about 99% of the speed of light, rendering them relativistic in high-energy decays.[12]Physical Properties
Beta particles, whether electrons (β⁻) or positrons (β⁺), carry an elementary charge of magnitude e = 1.602176634 \times 10^{-19} C, with β⁻ having a charge of -e and β⁺ a charge of +e.[13] This charge results in strong electromagnetic interactions with matter, primarily through Coulomb forces that lead to ionization and scattering as the particles traverse atomic fields.[14] The rest mass of a beta particle is m_e = 9.1093837015 \times 10^{-31} kg, corresponding to a rest energy of m_e c^2 = 0.51099895069 MeV.[15] In beta decay, beta particles acquire kinetic energies typically ranging from a few keV to several MeV, depending on the decaying nuclide, with the energy spectrum continuous and the maximum value determined by the Q-value of the decay.[14] For example, beta particles from phosphorus-32 have a maximum kinetic energy of 1.71 MeV.[14] Due to their low rest mass, beta particles quickly become relativistic even at modest kinetic energies, often approaching speeds v near the speed of light c. Their relativistic nature is quantified by the Lorentz factor \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}, which exceeds 2 for kinetic energies above about 1 MeV and leads to effects such as time dilation and length contraction in high-energy scenarios.[14] These properties influence the particles' trajectories and energy loss in materials. As fundamental leptons, beta particles possess an intrinsic spin angular momentum of s = \frac{1}{2} \hbar, where \hbar is the reduced Planck's constant, consistent with their classification as spin-1/2 fermions in the Dirac equation framework.[16] Upon slowing to rest, β⁺ particles (positrons) annihilate with ambient electrons, converting their combined rest masses into two gamma rays each of energy 0.511 MeV, emitted in opposite directions.[17]Beta Decay Processes
Negative Beta Decay
Negative beta decay, or β⁻ decay, occurs in atomic nuclei that have an excess of neutrons relative to protons, leading to instability. In this process, a neutron in the nucleus transforms into a proton, resulting in the emission of an electron (the β⁻ particle) and an electron antineutrino (ν̄_e). This transformation increases the atomic number by one while preserving the mass number, effectively converting one element into the next in the periodic table. The basic reaction is represented as: n \to p + e^- + \bar{\nu}_e This decay conserves key quantum numbers: baryon number remains 1 (neutron and proton each have baryon number 1), electric charge balances as 0 = +1 -1 + 0, and electron lepton number is conserved as 0 = 0 +1 -1 (where the antineutrino carries lepton number -1).[1][3] The energy released in negative beta decay, known as the Q-value, determines the total kinetic energy available to the products and is calculated using nuclear masses as: Q = \left[ m_N\left(^{A}_{Z}X\right) - m_N\left(^{A}_{Z+1}Y\right) - m_e \right] c^2 where m_N denotes nuclear mass and m_e is the electron rest mass. Equivalently, using atomic masses (which include electron bindings), the Q-value simplifies to Q = \left[ M\left(^{A}_{Z}X\right) - M\left(^{A}_{Z+1}Y\right) \right] c^2, accounting for the emitted electron. This energy is shared primarily between the electron and antineutrino as kinetic energy, with the daughter nucleus receiving negligible recoil in most cases; the electron's kinetic energy ranges from near zero up to a maximum of approximately Q (when the antineutrino carries minimal energy)./07%3A_Radioactive_Decay_Part_II/7.02%3A_Beta_Decay)[18] At a fundamental level, negative beta decay is governed by the weak nuclear force, mediated by the exchange of a charged W⁻ boson. In this interaction, a down quark in the neutron (udd) emits a W⁻, transforming into an up quark (uud, forming a proton), while the W⁻ subsequently decays into the electron and antineutrino. This process violates parity conservation but occurs at an introductory level without delving into detailed quark dynamics.[11][19] Prominent examples include the decay of carbon-14, used in radiocarbon dating: ^{14}_{6}\text{C} \to ^{14}_{7}\text{N} + e^- + \bar{\nu}_e, with a maximum electron kinetic energy of 0.156 MeV and a half-life of 5730 years. Another is tritium (hydrogen-3) decay: ^{3}_{1}\text{H} \to ^{3}_{2}\text{He} + e^- + \bar{\nu}_e, featuring a low maximum electron energy of 18.6 keV and a half-life of 12.32 years, making it useful in fusion research and neutrino mass experiments. The emission of beta particles was first observed by Henri Becquerel in 1896 during his studies of uranium salts, marking the discovery of radioactivity; the underlying mechanism, including the antineutrino's role, was clarified in the 1930s through theoretical and experimental advancements.[20][21][22][6]Positive Beta Decay
Positive beta decay, also known as β⁺ decay or positron emission, occurs in proton-rich atomic nuclei where a proton transforms into a neutron, emitting a positron (e⁺) and an electron neutrino (ν_e) to maintain conservation laws.[1] This process was theoretically predicted in 1928 by Paul Dirac through his relativistic quantum equation for the electron, which implied the existence of a positively charged counterpart to the electron.[23] The positron was experimentally discovered in 1932 by Carl Anderson during cosmic ray studies, confirming Dirac's prediction.[23] The fundamental reaction in positive beta decay is represented by the transformation of a proton within the nucleus:p \rightarrow n + e^+ + \nu_e
This weak interaction process shares conceptual similarities with negative beta decay in terms of the Q-value, defined as the atomic mass difference between parent and daughter nuclides converted to energy.[24] However, for β⁺ decay to be energetically feasible, the Q-value must exceed 1.022 MeV, equivalent to twice the rest mass energy of an electron (2m_e c²), accounting for the creation of the positron-electron pair during subsequent annihilation.[25] The available decay energy is partitioned between the positron's kinetic energy and the neutrino's energy, with the neutrino carrying away variable amounts to ensure three-body kinematics.[1] Representative examples include the decay of fluorine-18 (¹⁸F), a proton-rich isotope used in medical imaging:
^{18}\text{F} \rightarrow ^{18}\text{O} + e^+ + \nu_e
This decay proceeds with 96.7% branching ratio via positron emission, transforming the nucleus from Z=9 to Z=8 while conserving mass number A=18.[26] Another example is sodium-22 (²²Na), which decays primarily by positron emission (89.6% branching ratio):
^{22}\text{Na} \rightarrow ^{22}\text{Ne} + e^+ + \nu_e
followed by excited state transitions in the daughter neon nucleus.[27] Unlike electron capture, where a proton absorbs an inner-shell orbital electron to form a neutron and neutrino without emitting a charged particle, positive beta decay produces a detectable positron that can be observed directly in experiments./Nuclear_Chemistry/Radioactivity/Nuclear_Decay_Pathways) This distinction arises because β⁺ decay requires sufficient nuclear energy release to create the positron, whereas electron capture has no such charged particle emission.[24]