Beta decay was initially associated with the emission of an electron $\text{e}{}^{-}$, the beta particle. It was later discovered that some nuclei can undergo beta decay by emitting a positron $\text{e}{}^{+}$, the antiparticle of the electron, although this decay mode is not as common. A positron is identical to an electron except that it has a positive charge. To be precise, the emission of an electron is called beta-minus decay and the emission of a positron is beta-plus decay.

A typical example of beta-minus decay occurs in the carbon isotope ${}^{14}\text{C}$, which undergoes the beta-decay process ${}^{14}\text{C}{\to }^{14}\text{N}+{\text{e}}^{-}$. Carbon has $Z=6$ and nitrogen has $Z=7$. Because $Z$ increases by 1 but $A$ doesn’t change, it appears that a neutron within the nucleus has changed itself into a proton and an electron. That is, the basic beta-minus decay process appears to be

Indeed, a free neutron turns out not to be a stable particle. It decays with a half-life of approximately 10 min into a proton and an electron. This decay is energetically allowed because $m_{\text{n}}>m_{\text{p}}+m_{\text{e}}$. Furthermore, it conserves charge.

Whether a neutron within a nucleus can decay depends on the masses of the parent and daughter nuclei. The electron is ejected from the nucleus in beta-minus decay, but the proton is not. Thus the decay process shown in FIGURE 42.20a is

Energy is released because the mass decreases in this process, but we have to be careful when calculating the mass loss. Although not explicitly shown in Equation 42.17, the daughter ${}^A\text{Y}$ is actually the ionized atom ${}^A\text{Y}{}^{+}$ because it gained a proton but didn’t gain an orbital electron. Its mass is the atomic mass of ${}^A\text{Y}$ minus the mass of an electron. But the full right-hand side of the reaction includes an additional electron, the beta particle, so the total mass of the decay products is simply the atomic mass of ${}^A\text{Y}$.

FIGURE 42.20 Beta decay.

Full Alternative Text

Consequently, the energy released in beta-minus decay, based on the mass loss, is

The energy release has to be positive, so we see that beta-minus decay occurs only if $m_{\text{X}}>m_{\text{Y}}{\text{. }}^{14}\text{C}$ can undergo beta-minus decay to ${}^{14}\text{N}$ because $m({}^{14}\text{C})>m{(}^{14}\text{N})$. But $m({}^{12}\text{C) }<m{(}^{12}\text{N})$, so ${}^{12}\text{C}$ is stable and its neutrons cannot decay.

Beta-plus decay is the conversion of a proton into a neutron and a positron:

The full decay process, shown in FIGURE 42.20b, is

Beta-plus decay does not happen for a free proton because $m_{\text{p}}<m_{\text{n}}$. It can happen within a nucleus as long as energy is conserved for the entire nuclear system.

In our earlier discussion of Figure 42.11 we noted that the ${}^{12}\text{B}$ and ${}^{12}\text{N}$ nuclei could reach a lower energy state if a proton could change into a neutron, and vice versa. Now we see that such a change can occur if the energy conditions are favorable. And, indeed, ${}^{12}\text{B}$ undergoes beta-minus decay to ${}^{12}\text{C}$ while ${}^{12}\text{N}$ undergoes beta-plus decay to ${}^{12}\text{C}$.

In general, beta decay is a process used by nuclei with too many neutrons or too many protons in order to move closer to the line of stability in Figure 42.4.

A third form of beta decay occurs in some nuclei that have too many protons but not enough mass to undergo beta-plus decay. In this case, a proton changes into a neutron by “capturing” an electron from the innermost shell of orbiting electrons (an $n=1\text{\hspace{0.17em}electron}$). The process is

This form of beta decay is called electron capture, abbreviated EC. The net result, ${}^A\text{X}{}_Z{\to }^A\text{Y}{}_{Z-1}$, is the same as beta-plus decay but without the emission of a positron. Electron capture is the only nuclear decay mechanism that involves the orbital electrons.