Radioactive Decays

Most naturally occurring nuclei are perfectly stable, remaining unchanged indefinitely. But many others are not: they spontaneously transform, emitting some particle in the process and changing into a nucleus with a different mass number and/or atomic number. This phenomenon, radioactive decay (or radioactivity), was discovered in 1896 by Henri Becquerel and its name was later coined by Marie Curie, who went on (with her husband Pierre) to discover the elements radium and polonium. The original, unstable nucleus is called the parent nucleus, and the (generally more stable) nucleus produced by the decay is called the daughter nucleus. Radioactive decays fall into three distinct types.

In alpha decay, the parent nucleus ejects an alpha particle -- essentially a helium nucleus, i.e. a tightly bound cluster of two protons and two neutrons -- so the parent loses two units of atomic number and four units of mass number: $_Z^AX\rightarrow\,_{Z-2}^{A-4}Y+\,_2^4He$. This mode is common among the heaviest nuclei (roughly A > 210), whose large number of mutually repelling protons makes the nucleus increasingly unstable, since the electrostatic repulsion grows faster (with more protons) than the short-range nuclear force can compensate for; ejecting an alpha particle is an efficient way for such a nucleus to shed both protons and neutrons at once and move toward greater stability. The energy released, or Q-value, of the decay is $Q=[m_X-m_Y-m_{He}]c^2$, appearing as kinetic energy shared between the alpha particle and the (much heavier, so much more slowly recoiling) daughter nucleus.

In beta decay, a NUCLEON inside the nucleus itself transforms into a different kind of nucleon. In ordinary ($\beta^-$) beta decay, a neutron converts into a proton, an electron and an (electrically neutral, almost massless) antineutrino: $n\rightarrow p+e^-+\bar\nu$; the mass number A stays fixed (a nucleon is neither created nor destroyed, just converted) while Z increases by one, $_Z^AX\rightarrow\,_{Z+1}^AY+e^-+\bar\nu$. In the related $\beta^+$ (positron) decay, a proton instead converts into a neutron, emitting a positron (the electron's positively charged antiparticle) and a neutrino: $p\rightarrow n+e^++\nu$, so here Z DECREASES by one, $_Z^AX\rightarrow\,_{Z-1}^AY+e^++\nu$. Because a free proton's rest mass is slightly LESS than a free neutron's, this particular conversion is actually impossible for an isolated proton sitting on its own -- it can only happen for a proton bound INSIDE a nucleus, which can supply the small extra energy needed from the rest of the nuclear binding energy. Both forms release energy shared mainly between the emitted electron/positron and the neutrino/antineutrino, with $Q=[m_X-m_Y-m_e]c^2$ giving the MAXIMUM possible kinetic energy of the emitted electron or positron (reached in the limiting case where the neutrino or antineutrino carries away essentially no energy). …