Beta Minus vs Beta Plus Decay: Key Differences and ExamplesBeta decay is a type of radioactive decay that transforms an unstable nucleus by converting one type of nucleon into another while emitting a beta particle (an electron or positron) and an associated neutrino or antineutrino. Beta decay plays a central role in nuclear physics, astrophysics, nuclear medicine, and radiometric dating. The two primary varieties are beta minus (β−) decay and beta plus (β+) decay. This article compares them in detail, explains the underlying physics, provides representative examples, and discusses their applications and detection.
Basic definitions
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Beta minus (β−) decay: A neutron in the nucleus transforms into a proton, emitting an electron (beta particle) and an electron antineutrino: n → p + e− + ν̅_e
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Beta plus (β+) decay (positron emission): A proton in the nucleus transforms into a neutron, emitting a positron (the electron’s antiparticle) and an electron neutrino: p → n + e+ + ν_e
Fundamental differences
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Particle change in the nucleus
- β−: Neutron → Proton (neutron-rich nuclei move toward stability)
- β+: Proton → Neutron (proton-rich nuclei move toward stability)
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Emitted beta particle
- β−: Electron (e−)
- β+: Positron (e+)
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Associated (anti)neutrino
- β−: Electron antineutrino (ν̅_e)
- β+: Electron neutrino (ν_e)
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Effect on atomic number (Z) and mass number (A)
- β−: Z increases by 1; A unchanged
- β+: Z decreases by 1; A unchanged
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Energy considerations
- β−: Usually requires that the parent nucleus has higher mass-energy than the daughter (mass difference supplies kinetic energy).
- β+: Requires at least 1.022 MeV of energy (2 × electron rest mass) in addition to the nuclear mass difference, because creating a positron–electron pair costs 1.022 MeV. Thus fewer nuclides can decay via β+ than via β−; many proton-rich nuclides instead decay by electron capture.
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Competing process with similar net effect
- For proton-rich nuclei where β+ is energetically forbidden, electron capture (EC) often occurs: a bound electron (typically from the K-shell) is captured by a proton, converting it to a neutron and emitting a neutrino: p + e−_bound → n + ν_e
Underlying weak interaction and Feynman-picture notes
Beta decay is mediated by the weak nuclear force via W bosons at the fundamental level:
- β−: A down quark in a neutron changes to an up quark by emitting a W− boson; the W− then decays to e− + ν̅_e.
- β+: An up quark in a proton changes to a down quark by emitting a W+ boson; the W+ decays to e+ + ν_e.
These quark-level changes conserve charge, lepton number, energy, and other quantum numbers appropriate to the process.
Energy spectra and kinematics
- Beta decay is a three-body decay (daughter nucleus, beta particle, neutrino), so the emitted beta particle has a continuous energy spectrum from near zero up to a characteristic maximum endpoint energy (Qβ).
- The maximum kinetic energy of the beta particle equals the decay Q-value minus the recoil energy of the daughter nucleus (negligible for heavy nuclei). For β+, the Q-value must exceed 1.022 MeV for the decay to be allowed.
- The neutrino carries off a variable portion of the decay energy; its detection requires specialized detectors and inverse processes (e.g., inverse beta decay).
Examples
Beta minus decay examples:
- 14C → 14N + e− + ν̅_e
- Q ≈ 0.156 MeV, half-life ≈ 5,730 years. Used for radiocarbon dating.
- 90Sr → 90Y + e− + ν̅_e
- β− emitter; 90Sr (t1/2 ≈ 28.8 years) is a fission product and a health hazard.
- 131I → 131Xe + e− + ν̅_e
- Important in nuclear medicine and fallout; 131I decays by β− plus gamma emissions.
Beta plus decay examples:
- 22Na → 22Ne + e+ + ν_e
- Q ≈ 2.842 MeV, half-life ≈ 2.6 years. 22Na is used as a positron source; positron annihilation produces two 511 keV gamma photons used in detector calibration.
- 18F → 18O + e+ + ν_e
- Q ≈ 0.633 MeV (above 1.022 MeV requirement? Note: effective Q for positron emission from 18F is about 0.633 MeV available as kinetic energy for positron because nuclear mass difference accounts; 18F is a common PET radiotracer with t1/2 ≈ 110 minutes). [See note below about effective Q and positron threshold; some tables quote different values depending on atomic vs nuclear mass conventions.]
Electron capture examples (competes with or replaces β+ when energetically favored):
- 7Be + e− → 7Li + ν_e
- Important in solar neutrino production.
- 55Fe + e− → 55Mn + ν_e
Detection signatures and applications
- β− emitters: detected via beta particles (electrons) and often associated gamma emissions; used in radioisotope thermoelectric generators (RTGs have different decay types), industrial gauges, and some medical therapies (e.g., 90Y therapy).
- β+ emitters: positrons annihilate with electrons producing two 511 keV gamma photons emitted nearly back-to-back; this is the basis of positron emission tomography (PET) in medical imaging (e.g., 18F-FDG).
- Electron capture: produces characteristic X-rays or Auger electrons as atomic shells rearrange after the captured electron is removed; used in some medical and geophysical tracers.
Common misconceptions
- Positrons are not “anti-electrons” in some qualitative sense — they are the electron’s antiparticle with identical mass and opposite charge. When a positron meets an electron, annihilation produces gamma photons.
- Beta decay does not change the atomic mass number A; it changes the atomic number Z by ±1.
- Beta decay is not photon emission (gamma decay) — gamma decay involves de-excitation of the nucleus without changing Z or A.
Role in astrophysics and nucleosynthesis
- β-decays enable movement along isotopic chains during stellar nucleosynthesis and supernova processes. For example, the r-process (rapid neutron capture) path relies on beta decays of very neutron-rich nuclei to move material back toward stability, producing heavy elements.
- β+ decay and electron capture shape the proton-rich side of nuclear charts and play roles in nova and X-ray burst nucleosynthesis.
Simple comparison table
| Feature | Beta minus (β−) | Beta plus (β+) |
|---|---|---|
| Nuclear change | n → p | p → n |
| Emitted beta | Electron (e−) | Positron (e+) |
| Neutrino type | Electron antineutrino (ν̅_e) | Electron neutrino (ν_e) |
| Change in Z | +1 | −1 |
| Mass number A | unchanged | unchanged |
| Energy threshold | No pair-creation threshold | Requires ≥ 1.022 MeV (pair creation) |
| Common alternatives | — | Electron capture (if β+ forbidden) |
| Typical applications | Radiocarbon dating, therapy, fallout studies | PET imaging, positron sources |
Mathematical note: Q-value and energetics
The Q-value of a beta decay equals the mass difference between parent and daughter atoms (including electrons) converted to energy:
Q = [M_parent − M_daughter] c^2
For β+ decay, because a positron of mass m_e is created, the minimum nuclear mass difference must satisfy:
Q_nuclear ≥ 2 m_e c^2 ≈ 1.022 MeV
In three-body decays, the beta particle energy spectrum f(E) is shaped by phase space and nuclear matrix elements; for allowed transitions, the differential decay rate is proportional to:
dΓ/dE ∝ F(Z, E) p E (Q − E)^2
where E and p are the beta particle’s total energy and momentum, and F(Z, E) is the Fermi function accounting for Coulomb effects between beta particle and nucleus.
Practical considerations and safety
- Beta radiation (especially high-energy beta particles) can penetrate skin to some extent; shielding often uses low-Z materials (plastic, glass) to avoid producing bremsstrahlung X-rays that arise when betas are stopped by high-Z shielding like lead.
- Positron emitters require careful handling because annihilation photons are penetrating; shielding and distance protocols similar to gamma emitters apply.
- Radiological safety and regulatory controls govern production, transport, and medical use of beta-emitting isotopes.
Summary
Beta minus and beta plus decays are mirror processes driven by the weak interaction: β− converts neutrons to protons and emits electrons plus antineutrinos, while β+ converts protons to neutrons and emits positrons plus neutrinos. They differ in emitted particle charge, energy thresholds (β+ requires creating a positron), typical occurrence on different sides of the valley of stability, and practical detection signatures (positron annihilation versus direct electron emission). Both are central to nuclear physics, medical imaging, radiometric dating, and astrophysical nucleosynthesis.
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