Beta (β) Decay

  April 09, 2022   Read time 5 min
Beta (β) Decay
Beta decay occurs in a nucleus that has too many protons or too many neutrons for stability.

One of the excess neutrons (or protons) transforms itself into the other type of nucleon, producing a change in the proton-toneutron (Z/N) ratio that moves the daughter nuclide closer to the region of nuclear stability shown in Figure 4.7. Beta particles are electrons or positrons (electrons with a positive charge) that emerge from the atomic nucleus as a result of this decay process. There are several types of beta decay: beta-minus decay, beta-plus decay, and electron capture.

In beta-minus (β−) decay, a neutron within the nucleus of the parent radionuclide spontaneously transforms into a positively charged proton. As a result of this decay process, a negatively charged electron (called the beta minus particle [β−]) and an elusive, elementary particle (the electronantineutrino [ − νe]) simultaneously appear and are emitted from the nucleus. The emitted leptons (the electron and the antineutrino) did not exist as distinctive elementary particles in the nucleus before the beta-minus decay process. Instead, they are created at the instant of beta decay and then leave the transforming nucleus. Equation 4.18 presents the nuclear reaction shorthand for beta-minus decay—an important radioactive decay phenomenon in which an atomic nucleus seeks nuclear stability by converting one of its excess neutrons into a proton.

Several conservation laws are at work here. The conservation of electric charge requires that if an electrically neutral neutron becomes a positively charged proton, then an electrically negative particle (in this case, an electron) must also be created. Similarly, the conservation of lepton number principle requires that if a neutron (lepton number = 0) decays into a proton (lepton number = 0) and an electron (lepton number = 1), then a neutral elementary particle of negligible mass with a lepton number of –1 (here, the electron-antineutrino [ν¯e]) must also appear.
Neutrinos are very elusive elementary particles that play an interesting scientific role in high-energy nuclear physics, nuclear astronomy, and modern cosmology. The neutrino has no charge, negligible mass, and interacts with matter only through what physicists call the weak force—that is, the force responsible for beta decay. This force is so weak that a neutrino can pass through a person’s body with negligible chance of causing ionization. First postulated by Pauli, the elementary particle received its current name from Enrico Fermi (1901–1954), who suggested the term neutrino ( “little neutral one” in Italian), while he was developing his theory of beta-minus decay. Because neutrinos do not interact significantly with ordinary matter, their existence and presence is generally ignored in technical discussions concerning the practical applications of nuclear technology. Consequently, the treatment of neutrinos is limited in this book. For example, consistent with contemporary nuclear technology practices, it is reasonable to assume that when radioactive nuclei undergo beta decay only the electron (beta particle) is detected and only the electron causes biological effects.
In beta-minus decay, a neutron in the nucleus transforms into a proton and an electron. The daughter nucleus experiences no change in atomic mass number (A) but its atomic number (Z) increases by one, turning the decay-product nuclide into another chemical element. Scientists use the following notation to describe the nuclear consequences of the general beta-minus decay process. (We are excluding the electron-antineutron here.)
Of special significance is the fact that the atomic number (Z) of the daughter nuclide increases by one, transforming the atom into another chemical element. However, the total nucleon or atomic mass number (A) of the daughter nuclide remains the same as that of the parent nuclide. Beta decay is a considerably different nuclear transformation than alpha decay, in which the atomic number of the daughter decreases by two while the nucleon number decreases by four.
In beta decay, the change in the binding energy appears as the energy equivalent mass and kinetic energy of the beta particle, the energy of the antineutrino or neutrino, and the kinetic energy of the recoiling daughter nucleus. Because this energy can be shared in many ways among the three resultant particles in a statistical manner that obeys the conservation of energy and conservation of momentum principles, the emitted beta particle has a continuous kinetic energy distribution that goes from zero energy to some maximum value, called the endpoint energy. Nuclear scientists find it convenient to characterize the range of beta particle energies for a particular radioactive isotope by specifying the maximum beta energy (βmax) and the average beta energy (βave).
One of the more important beta-minus emitters in nuclear technology is the radioactive isotope of hydrogen, tritium (3 1H). The tritium nucleus contains two neutrons and one proton and has a half-life of 12.3 years. This radionuclide undergoes beta-minus decay as follows: 3 1H → 3 2He + 0 –1β. The beta minus (β−) particle for the decay of tritium has a maximum value of 0.018 MeV (βmax) and an average value of 0.006 MeV. Figure 4.15 describes the distribution of energies of the beta particles associated with the decay of tritium. The daughter nuclide is the rare, but stable, isotope helium-3 (3 2He). The maximum energy beta particle emitted when tritium decays is only 18 kiloelectron volts (keV), making it considerably less energetic than the 5 MeV alpha particle emitted when plutonium-239 decays. The average beta particle (about 6 keV) from tritium would, at most, generate about 150 ion pairs in either water or living tissue—compared with the approximately 150,000 ion pairs produced by a single alpha particle. Although the radioactive decay of tritium involves the emission of relatively low energy beta particles, if tritium gets into the human body, it can go everywhere because it is a form of hydrogen. Sufficient internal concentrations of tritium can then do significant ionization damage throughout all the cells of the body.

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