## 22.3.2 Beta Decay Beta decay is a type of radioactive decay in which an atomic nucleus emits a beta particle, which may be an electron or a positron. This emission causes the atomic number ($Z$) of the nucleus to change while the mass number ($A$) remains conserved. Beta decay is categorized into two main types: negative beta decay ($\beta^-$) and positive beta decay ($\beta^+$). Unlike alpha decay, which is governed by the strong nuclear force, beta decay is mediated by the **weak nuclear force**. ## i) Negative Beta ($\beta^-$) Decay In $\beta^-$ decay, an unstable nucleus emits an electron ($\beta^-$ particle) and an antineutrino ($\bar{\nu}$). The underlying process involves a neutron inside the nucleus decaying into a proton. At the subatomic level, a down quark within the neutron changes into an up quark. The equation for neutron decay is: $$\mathrm{n} \rightarrow \mathrm{p} + \,_{-1}^{0}\beta + \bar{\nu}$$ For nuclei, the general equation is: $${ }_{Z}^{A}\mathrm{X} \rightarrow { }_{Z+1}^{A}\mathrm{Y} + { }_{-1}^{0}\beta + \bar{\nu}$$ Here, $\mathrm{X}$ is the parent nucleus and $\mathrm{Y}$ is the daughter nucleus. The atomic number $Z$ increases by 1, while the mass number $A$ remains unchanged. ## ii) Positive Beta ($\beta^+$) Decay In $\beta^+$ decay, an unstable nucleus emits a positron ($\beta^+$ particle) and a neutrino ($\nu$). The underlying process involves a proton inside the nucleus decaying into a neutron. The equation for proton decay is: $$\mathrm{p} \rightarrow \mathrm{n} + { }_{+1}^{0}\beta + \nu$$ For nuclei, the general equation is: $${ }_{Z}^{A}\mathrm{X} \rightarrow { }_{Z-1}^{A}\mathrm{Y} + { }_{+1}^{0}\beta + \nu$$ Here, $\mathrm{X}$ is the parent nucleus and $\mathrm{Y}$ is the daughter nucleus. The atomic number $Z$ decreases by 1, while the mass number $A$ remains unchanged. ### Energy Spectrum and the Neutrino One of the historical puzzles of beta decay was the continuous energy spectrum of the emitted electrons. Unlike alpha particles, which are emitted with discrete energies (related to ), beta particles show a range of kinetic energies. To account for the "missing" energy and momentum, Wolfgang Pauli proposed the existence of the neutrino (or antineutrino). These particles are neutral, have nearly zero mass, and carry away the remaining energy and spin to satisfy conservation laws. ### Comparison Table | Feature | Beta-minus ($\beta^-$) Decay | Beta-plus ($\beta^+$) Decay | | :--- | :--- | :--- | | **Emitted particle** | Electron (${ }_{-1}^{0}\beta$) | Positron (${ }_{+1}^{0}\beta$) | | **Associated particle** | Antineutrino ($\bar{\nu}$) | Neutrino ($\nu$) | | **Nucleon change** | Neutron $\rightarrow$ Proton | Proton $\rightarrow$ Neutron | | **Atomic Number ($Z$)** | Increases by 1 ($Z \rightarrow Z+1$) | Decreases by 1 ($Z \rightarrow Z-1$) | | **Mass Number ($A$)** | Conserved | Conserved |