Radioactive Decay by Beta Particle Emission

Beta Radioactive Decay
Typical Energy Distribution for a ß- emitting nuclide during radioactive decay

This article describes the radioactive decay in the beta particle decay process, including a  discussion of average and end-point energies, and of neutrinos. The ultimate fate of beta particles after they expend all their kinetic energy is explained, as well as the relative positions of parent and daughter, or progeny, on the Chart of the Nuclides due to beta decay. Electron capture as an alternative to positron emission Is also covered.

Introduction

In all isotopes of elements lighter than polonium (Z = 84), radioactivity is due to the nucleus of a given atom having too many or too few neutrons, compared to the number of protons that it possesses. As for polonium and those elements heavier than polonium (e.g., radium, thorium, uranium, plutonium), there are no stable Isotopes. These heavy elements simply possess too much mass-energy for any stable neutron-proton configuration.

Many radioisotopes, both heavy and light, emit a beta particle during their decay process. In some Isotopes this particle is negatively charged and is referred to as a Beta Minus (ß-) or (infrequently) as a negatron. In other isotopes, this particle has a positive charge and is called a positron (ß+). As a general rule, a beta-emitting radioisotope decays either by ß- or by ß+ emission. There are a few exceptions to this rule (e.g., K-40 and 0-36 can decay by ß- or ß+), but most of these decay by one preferred path a large percentage of the time. For example, chlorine-36 decays by ß- in 99 percent of Its decays and ß+ 1 percent of the time.

Nuclear Origin of Beta Particles

Beta Minus. Since ß– particles originate in the nucleus of a decaying atom, and since we know that only protons (positively charged) and neutrons (no charge) inhabit the nucleus, the origin of this negatively charged particle may be in question. While we generally think of a neutron as an uncharged nuclear particle, in reality it possesses both negative and positive charge components, which exactly balance one another, making the neutron appear to have no charge. At the beginning of a ß- decay, one of the neutrons in the nucleus concentrates one electrostatic unit (ESU) of this negative charge component, then expels it along with a very small quantity of the mass of the neutron. That mass is 9.109534 E-28 grams, or 5.4858 E-4 atomic mass units (AMUs). The neutron is thus changed into a proton, and the daughter nucleus contains one fewer neutron and one more proton than the nucleus did before it decayed. Since ß- decay changes neutrons into protons in the radioactive nucleus, it is a decay mode which is characteristic of those isotopes which are radioactive because they have too many neutrons in their nuclei (i.e., the neutron-proton ratio is too high).

Positrons

The birth of a positron in the nucleus of a radioactive atom begins when one of the protons in the nucleus concentrates one ESU of this positive charge component, then expels it along with a very small quantity of the mass of the proton. The mass of the positron is the same as that of the ß-. The proton is thus changed into a neutron, and the daughter nucleus contains one fewer proton and one more neutron than did the nucleus which decayed. Since ß+ decay changes protons into neutrons in the radioactive nucleus, it is a decay mode which is characteristic of those isotopes which are radioactive because they have too many protons in their nuclei (i.e., the neutron-proton ratio is too low).

Neutrinos and Antineutrinos

Each time a beta particle is emitted, a second particle is also ejected. This second particle Is called a neutrino (Greek letter nu-v) In the case of ß+, and an antineutrino (v) in the case of a ß-. (The “antl-” prefix Indicates that it is paired with a negatively charged beta particle.) These neutrinos and antineutrinos have no charge and virtually no mass. They therefore deliver no radiation dose and are not detectable with standard field or laboratory detection equipment. They are, therefore, of no concern from a radiation protection perspective. We need them, however, to explain the variation in the measured beta particle energy from each beta-emitting nuclide.

Transition Energy

One requirement for the atoms of each radioisotope is that every radioactive decay event must get rid of precisely the same amount of energy.

This means that the sum total of the energies of the particles and photons coming out of a decay event must always be the same for the atoms of the same radioisotope. This quantity of energy is called the Q-value. This satisfies the requirement for the conservation of energy.

Beta particles are unique in that they are emitted by a given isotope over a wide range of energies from virtually zero up to some maximum or end-point value. (This is unlike alpha particles and gamma photons, which are emitted at precise or discrete energies for each possible decay mode for each isotope.) This maximum amount of energy is always present in each beta disintegration, but it is divided between the ß- and the antineutrino, or between the ß+ and the neutrino.

For instance, the Emax ß- energy from a Strontium-90 decay is 0.546 MeV. If the actual energy of a ß- from a Sr-90 decay is measured to be 0.125 MeV, then the antineutrino is emitted with an energy of 0.421 MeV (0.125 + 0.421 = 0.546 MeV). If the actual energy of another Sr-90 ß- is measured at 0.546 MeV (the Emax value), the antineutrino is emitted with zero energy. The Q-value for Sr-90 is 0.546 MeV. Since the ß-/v pair accounts for all of this transition energy, there is no energy left for the nucleus to get rid of. Therefore, Sr-90 is a pure beta emitter.

As another example, consider Neon-18, a positron emitter with Emax given as 3.42 MeV. If the measured energy of a particular positron is 2.45 MeV, then the neutrino was emitted with an energy of 0.97 MeV. The Q-value for Ne-18 is 4.45 MeV. Therefore, the excess energy (4.45 MeV -3.42 MeV = 1.03 MeV) is given off in the form of a gamma ray.

Note that any photon (gamma) energy coming out of a beta decay will be in addition to the beta energy. and will not influence the beta particle energy in any way.

Estimating Average Beta Energy

The widely accepted rule of thumb for estimating the average energy (Eav) of a ß- emitting Isotope is Eav ≈ Emax. Therefore, the estimated average energy of a Sr-90 beta minus is

Eav ≈ 1/3 (0.546 MeV) .. 0.182 MeV.

When estimating the average energy of positrons, the thumb rule becomes Eav ≈ 0.4 Emax. Therefore, the estimated average energy of a Ne-18 positron is

Eav ≈ (0.4) (3.42 MeV) ≈ 1.368 MeV.

An Alternative to Positron Emission

Chart of the NuclidesMany of the isotopes which decay by positron emission may also decay by another mechanism called electron capture. In the Chart of the Nuclides, electron capture is symbolized by the Greek letter “eta” (ϵ). In this radioactive decay mode, an orbital electron is captured by a proton in the nucleus. The negative charge on the electron neutralizes the positive charge on the proton, changing it into a neutron. The net result is the same as in a positron emission; the daughter nucleus has one fewer proton and one more neutron than did the parent nucleus. Since the captured electron is virtually always from the “k” (inner) shell, this decay mode is sometimes called “k-capture.” •

Two things need to be remembered with electron capture, however:

1)  No particle is ejected from the nucleus; and

2)  All Inner shell electron has been removed from its orbit. Each time an electron from an outer shell drops into an inner shell to fill an electron void, an x-ray is produced. Therefore, the only detectable emissions coming from electron capture decay are x-rays.

The Fate of Beta Particles

After a beta minus particle expends all of its kinetic energy (energy of motion), it simply becomes a free electron. It has the same mass as an electron and the same charge. It would not be correct, however, to call a ß- an electron.

Positrons are different. They are really particles of anti-matter, and cannot exist in this universe unless they possess kinetic energy (ie., are in motion). Once a positron loses its kinetic energy by interacting with the atoms of whatever materiel it is passing through, it will attract and combine with a free electron. As the two particles come together, the masses of both particles are completely annihilated and converted into energy in the form of two gamma rays. Since the mass of both the electron end the positron is 5.4858 E-4 atomic mass units (AMU), and given that the mass-to-energy conversion factor is 931 .5 MeV per AMU, then

5.4858 E -4 AMU X (931.5 MeV / AMU) = 0.511 MeV

The energy, then, of each of the two gamma rays formed by this annihilation event is 0.511 MeV or 511 keV. These 511 keV annihilation photons cause significant background interference in a gamma spectrometer.

Identifying Daughter Nuclides

Since positron decay reduces the number of protons in the decaying nucleus by one end increases the number of neutrons by one, the position of the daughter nucleus on the Chart of the Nuclides after this decay takes place Is one block down and one block to the right of the parent nucleus. For example, fluorine-17 decays by positron emission to oxygen-17, which is stable.

Beta minus decay, on the other hand, reduces the number of neutrons by one, and increases the number of protons by one. Therefore, the position of the daughter nucleus on the Chart of the Nuclides after this decay takes place is one position up and one position to the left of the parent nucleus. For example, Nitrogen-16 decays by ß- emission to Oxygen-16, which is stable.

Future Articles will provide more information on The Chart of the Nuclides, beta particle shielding, and bremsstrahlung x-ray production by beta particles.

Paul Steinmeyer is the founder and president of Radiation Safely Associates, Inc., and Editor-in-Chief of RSO Magazine.

Editor’s Note: The previous article is the first in a three-part series on beta radiation by our Editor-In-Chief, K. Paul Steinmeyer. Future articles will deal with beta particle shielding and bremsstrahlung. We encourage our readers to conflict US with any questions or comments” you have concerning these topics.

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