state that (electron) antineutrinos are produced during β– decay and (electron) neutrinos are produced during β+ decay

Published by Patrick Mutisya · 14 days ago

Cambridge A-Level Physics 9702 – Atoms, Nuclei and Radiation

Atoms, Nuclei and Radiation

Objective

State that (electron) antineutrinos are produced during β⁻ decay and (electron) neutrinos are produced during β⁺ decay.

Beta Decay Overview

Beta decay is a type of radioactive decay in which a nucleus changes its proton–neutron composition by emitting a beta particle (an electron or a positron) together with a (anti)neutrino. The two main modes are:

  • β⁻ decay (beta‑minus): a neutron is transformed into a proton.

  • β⁺ decay (beta‑plus): a proton is transformed into a neutron.

β⁻ Decay (Beta‑Minus)

In β⁻ decay a neutron inside the nucleus converts into a proton, emitting an electron (e⁻) and an electron antineutrino ( \$\bar{\nu}_e\$ ). The reaction can be written as

\$n \;\rightarrow\; p + e^- + \bar{\nu}_e\$

At the nuclear level this is expressed as

\$\;^{A}{Z}\!X \;\rightarrow\; ^{A}{Z+1}\!Y + e^- + \bar{\nu}_e\$

Key points:

  1. The emitted electron is called a beta particle.

  2. The electron antineutrino carries away excess energy and momentum, ensuring conservation of lepton number.

  3. Lepton number is conserved because the electron (lepton number +1) is balanced by the antineutrino (lepton number −1).

β⁺ Decay (Beta‑Plus)

In β⁺ decay a proton inside the nucleus converts into a neutron, emitting a positron (e⁺) and an electron neutrino ( \$\nu_e\$ ). The reaction is

\$p \;\rightarrow\; n + e^+ + \nu_e\$

At the nuclear level:

\$\;^{A}{Z}\!X \;\rightarrow\; ^{A}{Z-1}\!Y + e^+ + \nu_e\$

Key points:

  1. The emitted positron is the antiparticle of the electron.

  2. The electron neutrino carries away excess energy and momentum, again preserving lepton number.

  3. Lepton number is conserved because the positron (lepton number −1) is balanced by the neutrino (lepton number +1).

Comparison of β⁻ and β⁺ Decay

Featureβ⁻ Decayβ⁺ Decay
Change in nucleusn → p (Z + 1)p → n (Z − 1)
Emitted particleElectron (e⁻)Positron (e⁺)
Associated (anti)neutrinoElectron antineutrino ( \$\bar{\nu}_e\$ )Electron neutrino ( \$\nu_e\$ )
Lepton number balancee⁻ (+1) + \$\bar{\nu}_e\$ (−1) = 0e⁺ (−1) + \$\nu_e\$ (+1) = 0
Typical energy release\overline{0}.5–3 MeV (shared between e⁻ and \$\bar{\nu}_e\$)\overline{1}.022 MeV + kinetic energy (positron mass‑energy must be supplied)

Why the (Anti)neutrino Is Important

The (anti)neutrino ensures that the following conservation laws are satisfied in beta decay:

  • Conservation of lepton number.

  • Conservation of energy and momentum (the continuous beta‑particle energy spectrum is a result of the three‑body final state).

  • Conservation of angular momentum (spin).

Suggested diagram: Energy‑level diagram showing a neutron converting to a proton with the emission of an electron and an electron antineutrino (β⁻ decay) on the left, and a proton converting to a neutron with the emission of a positron and an electron neutrino (β⁺ decay) on the right.

Key Take‑away Statement

During β⁻ decay an electron antineutrino ( \$\bar{\nu}e\$ ) is emitted together with the electron, whereas during β⁺ decay an electron neutrino ( \$\nue\$ ) is emitted together with the positron.