State that electron antineutrinos (̄φe) are emitted in β⁻ decay and that electron neutrinos (φe) are emitted in β⁺ decay. In doing so you will see how the (anti)neutrino guarantees conservation of lepton number, energy, momentum and angular momentum.
| Radiation | Particle(s) emitted | Typical energy range | Representative nuclear equation |
|---|---|---|---|
| α‑radiation | α‑particle (42He) | 4–9 MeV | ⁽ᴬ⁾ZX → ⁽ᴬ⁻⁴⁾{Z‑2}Y + ^4_2He |
| β⁻‑radiation | Electron (e⁻) + electron antineutrino (̄φe) | 0.5–3 MeV (shared) | ⁽ᴬ⁾ZX → ⁽ᴬ⁾{Z+1}Y + e⁻ + ̄φe |
| β⁺‑radiation | Positron (e⁺) + electron neutrino (φe) | ≥1.022 MeV + kinetic | ⁽ᴬ⁾ZX → ⁽ᴬ⁾{Z‑1}Y + e⁺ + φe |
| γ‑radiation | Photon (γ‑ray) | 0.1–10 MeV (typical) | ⁽ᴬ⁾ZX* → ⁽ᴬ⁾ZX + γ |
⁽ᴬ⁾_ZX (mass number A, atomic number Z).All matter is built from two families of elementary particles:
uud, neutrons are udd.In β‑decay the weak interaction changes a down‑quark to an up‑quark (β⁻) or an up‑quark to a down‑quark (β⁺) and creates the appropriate lepton–neutrino pair.
An isotope is written ⁽ᴬ⁾_ZX, where:
Atomic masses are given in unified atomic mass units (u), with 1 u = 931.5 MeV c⁻². The mass‑defect Δm is the difference between the sum of the individual nucleon masses and the measured nuclear mass; the binding energy B = Δm c².
n → p + e⁻ + ̄φe
⁽ᴬ⁾ZX → ⁽ᴬ⁾{Z+1}Y + e⁻ + ̄φe
⁽¹⁴⁾6C → ⁽¹⁴⁾7N + e⁻ + ̄φe
Atomic masses (to 5 dp):
Q‑value:
\[
\begin{aligned}
Q &= \bigl[m(^{14}\!C)-m(^{14}\!N)-m_e\bigr]c^{2} \\
&= (0.0001194\;\text{u})\times 931.5\;\text{MeV/u} \\
&\approx 0.11\;\text{MeV}.
\end{aligned}
\]
Because the decay is a three‑body process, the kinetic energy is shared continuously between the electron and the antineutrino, producing the characteristic continuous β‑spectrum (0 → Q).
p → n + e⁺ + φe
⁽ᴬ⁾ZX → ⁽ᴬ⁾{Z‑1}Y + e⁺ + φe
⁽²²⁾11Na → ⁽²²⁾10Ne + e⁺ + φe
Atomic masses:
Q‑value:
\[
\begin{aligned}
Q &= \bigl[m(^{22}\!Na)-m(^{22}\!Ne)-2m_e\bigr]c^{2} \\
&= (0.001994\;\text{u})\times 931.5\;\text{MeV/u} \\
&\approx 1.86\;\text{MeV}.
\end{aligned}
\]
The first 1.022 MeV supplies the rest‑mass energy of the e⁺e⁻ pair; the remaining energy appears as kinetic energy of the positron and the neutrino.
| Feature | β⁻ decay | β⁺ decay |
|---|---|---|
| Quark change | d → u | u → d |
| Nuclear change | n → p (Z + 1) | p → n (Z – 1) |
| Lepton emitted | Electron e⁻ | Positron e⁺ |
| Associated (anti)neutrino | Electron antineutrino ̄φe | Electron neutrino φe |
| Lepton‑number balance | +1 + (–1) = 0 | –1 + (+1) = 0 |
| Typical Q‑value | 0.5–3 MeV (continuous spectrum) | ≥1.022 MeV + kinetic |
| Detectable radiation | Electron track in cloud/chamber; antineutrino undetected. | Positron track + two 511 keV annihilation γ‑rays; neutrino undetected. |
⁽ᴬ⁾ZX → ⁽ᴬ⁻⁴⁾{Z‑2}Y + ^4_2He. Conserves A and Z; releases 4–9 MeV.⁽ᴬ⁾ZX* → ⁽ᴬ⁾ZX + γ. No change in A or Z; photon energy equals the difference between nuclear energy levels.For any nuclear transformation
\[
Q = \bigl[M{\text{initial}}-M{\text{final}}\bigr]c^{2},
\]
where the masses are taken from atomic‑mass tables (including the electrons that belong to neutral atoms).
Binding energy per nucleon B/A is obtained from the total mass‑defect of the nucleus and helps explain why very light nuclei favour β⁺ decay and very heavy nuclei favour α decay.
During β⁻ decay a neutron converts to a proton and emits an electron (e⁻) together with an electron antineutrino (̄φe). During β⁺ decay a proton converts to a neutron and emits a positron (e⁺) together with an electron neutrino (φe). The (anti)neutrino ensures that lepton number, energy, momentum and angular momentum are all conserved.
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