9.8.C - Radioactive Decay

Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionising particles (ionizing radiation). A decay, or loss of energy, results when an atom with one type of nucleus, called the parent nucleus, transforms to an atom with a nucleus in a different state, or to a different nucleus containing different numbers of protons and neutrons. Either of these products is named the daughter nucleus. In some decays the parent and daughter are different chemical elements, and thus the decay process results in nuclear transmutation (creation of an atom of a new element).

The first decay processes to be discovered were alpha decay, beta decay and gamma decay. Alpha decay occurs when the nucleus ejects an alpha particle (helium nucleus). Beta decay occurs when the nucleus emits an electron or positron and a type of neutrino, in a process that changes a proton to a neutron or the other way around.

By contrast, there exist radioactive decay processes that do not result in transmutation. The energy of an excited nucleus may be emitted as a gamma ray in gamma decay, or used to eject an orbital electron by interaction with the excited nucleus in a process called internal conversion.

In this unit you will:

  • Explain those fatcors that affect the stability of nucleus
  • Describe the three common types of radioative decay: alpha, beta and gamma decay
  • Write write nuclear equations to show these decay processes
  • Identify some medical and industrial uses of radioisotopes

The Nucleus

Atomic notation for an
isotope of carbon.

An atom consists of an extremely small, positively charged nucleus surrounded by a cloud of negatively charged electrons. Although typically the nucleus is less than one ten-thousandth the size of the atom, the nucleus contains more that 99.9% of the mass of the atom.

Nuclei consist of positively charged protons and electrically neutral neutrons held together by the so called strong nuclear force. This force is much stronger than the repulsive electrostatic (Coulomb) force, but its range is limited to distances on the order of a few (10-15) metres.

The number of protons in the nucleus, Z, is called the atomic number. This determines what chemical element the atom is. The letter N denotes the number of neutrons in the nucleus. The atomic mass of the nucleus, A, is equal to Z + N and gives the total number of nuclear particles in the nucleus which are collectively referred to as nucleons.


A given element can have many different isotopes, which differ from one another by the number of neutrons contained in the nuclei. In a neutral atom, the number of electrons orbiting the nucleus equals the number of protons in the nucleus. Since the electric charges of the proton and the electron are +1 and -1 respectively, the net charge of the atom is zero. At present, there are 118 known elements that range from the lightest, hydrogen, to the recently discovered and yet to-be-named element 118.

All of the elements heavier than uranium (Z = 92) are synthesised in particle accelerators. Among the elements are approximately 270 stable isotopes, and more than 2000 unstable isotopes. All isotopes of elements above lead (Z = 82) are unstable. Unstable isotopes are called radioisotopes.

The existence of isotopes is evidence for the existence of neutrons because there is no other way to explain the mass difference of two isotopes of the same element. By definition, two isotopes of the same element must have the same number of protons, which means that the mass attributed to those protons must be the same. Therefore, there must be some other particle that accounts for the difference in mass, and that particle is the neutron.

Forces within the Nucleus

Graph showing the strong nuclear force between nucleons as a function
of the separation of the nucleons.

The protons in the nucleus are all positive. Since like charges repel, they must be repelling one another all of the time. This means that there must be another force in the nucleus keeping it together. Without it the nucleus would 'fly apart'. The following are some things that we know about this force.

  • It must strong. If the proton repulsions are calculated it is clear that the gravitational attraction between the nucleons is far too small to be able to keep the nucleus together.

  • It must be very short-ranged, as we do not observe this force anywhere but in the nucleus.

  • It is likely to involve the neutrons as well. Small nuclei tend to have equal numbers of protons and neutrons. Large nuclei need proportionately more neutrons to keep the nucleus together.

From the graph we can see that the strong nuclear force is repulsive at very small distances and then becomes attractive at larger distances before tapering off to small attractive force values after about
2.5 x 10-15 m. If the distance between the nucleons is too large, the repulsive force between the protons cause the nuclei to be unstable.

Nuclear Stability

Two isotopes of carbon.

Some atoms are stable and others are unstable, depending on the balance of protons and neutrons in their nucleus. For example, not all carbon atoms are the same, since the number of neutrons they have can vary. Some carbon atoms have six protons and six neutrons (carbon-12). Another type has six protons and 8 neutrons (carbon-14). When the Coulomb force and the strong nuclear force are not balanced, the nucleus has a tendency to break-up spontaneously producing nuclei of other elements. These atoms break up spontaneously and in doing so they give off high-energy radiation. This spontaneous break-up of atoms is called radioactive decay and it generally occurs in elements whose nuclei are unstable. Those isotopes of elements that are unstable and undergo radioactive decay are called radioisotopes.

A graph with the proton-neutron ratio of all of the
known stable isotopes plotted which forms the belt
of stability.

The stability of a particular nucleus depends on a variety of factors and no single rule allows us to predict whether a particular nucleus is radioactive. There are, however, several empirical observations that will help us to make some predictions.

All nuclei with two or more protons contain neutrons. The more protons packed into the nucleus, the more neutrons are needed to bind the nucleus together. Stable nuclei with low atomic numbers (up to about 20) have approximately equal numbers of protons and neutrons. For nuclei with higher atomic numbers, the number of neutrons exceeds the number of protons. Indeed, the number of neutrons necessary to create a stable nucleus increases more rapidly than the number of protons as shown in the diagram on the right. Thus the neutron-to-proton ratios of stable nuclei increase with increasing atomic number.

The coloured band in the centre of the graph, within which all stable nuclei are found, is called the belt of stability. It stops at element 82 (lead) because all nuclei with more than 82 protons are radioactive. For example, all isotopes of uranium are radioactive because they have atomic numbers greater than 83.

Radioactive elements will undergo decay to move into the belt of stability. Generally, nuclei above the belt of stability (high neutron-to-proton ratio) will undergo beta minus decay to reduce the number of neutrons and increase the number of protons. Nuclei below the belt of stability (low neutron-to-proton ratio) will undergo beta plus decay to decrease the number of protons and increase the number of neutrons. Those heavier elements with atomic numbers greater than 83 tend to undergo alpha decay. The emission of an alpha particle decreases both the number of neutrons and the number of protons by two.


Radioactive Decay

The excess energy is carried away from an unstable nucleus
as kinetic energy of particles or as gamma ray photons.

Transmutation is the name given to the process that results in an atom changing its proton number and hence its identity. This can happen during radioactive decay with the emission of a particle from the nucleus, through fission when a nucleus breaks into two smaller nuclei, through the capture of a particle into the nucleus or through fusion when two nuclei collide and combine. Transmutation can occur naturally when nuclei decay to produce alpha, beta or gamma radiation or artificially by bombarding a nucleus with a particle such as a proton, neutron, electron or other nucleus. In this section we look at the natural radioactive decay of unstable isotopes.

A radioisotope has an unstable nucleus and therefore an excess of energy. Radioactive decay is an exothermic process because energy is released by the nucleus. The mass of the product nuclei is smaller than the mass of the decaying nuclei and the mass lost is converted into energy given by E = mc2. The energy is carried away from the nucleus as kinetic energy by a moving particle (as in alpha and beta decay) or as a gamma ray photon (in gamma decay).

Alpha Decay

Alpha decay of plutonium-240 into uranium-236 and an alpha particle.

Alpha particles are emitted during the decay of certain types of radioactive materials. Compared to other types, the alpha particle has a relatively large mass. It consists of two protons and two neutrons making the alpha particle the same as a helium nucleus. It is a highly charged particle that is emitted from the nucleus of an unstable atom. The positive charge causes the alpha particle to strip electrons from nearby atoms as it passes through the material, thus ionising these atoms. This is why alpha radiation is called ionising radiation because it has the ability to ionise the materials that it passes through. When a nucleus undergoes alpha decay, the energy released is carried away by the alpha particle as the nucleus breaks up. The alpha particle loses a large amount of energy in a short distance of travel. This large energy deposit limits the penetrating ability of the alpha particle to a very short distance. Most alpha particles are stopped by a few centimetres of air, a sheet of paper, or the dead layer (outer layer) of skin on our bodies. Alpha particles are not considered an external radiation hazard. This is because the dead layer of skin easily stops them. If alpha emitting radioactive material is inhaled or ingested, it becomes a source of internal exposure. Internally, the source of the alpha radiation is in close contact with body tissue and can deposit large amounts of energy in a small volume of body tissue.

Beta Decay

Beta minus decay of radium-228 into uranium-228, an electron
and an antineutrino.

The beta particle is an energetic electron emitted during radioactive decay. Compared to an alpha particle, a beta particle is nearly 8000 times smaller and has half the electrical charge. Beta radiation causes ionisation by the same forces at work with alpha radiation - mainly electrical interactions with atoms that are encountered as it travels. However, because it is not as highly charged, the beta particle is not as effective at causing ionisation. Therefore, it travels further before giving up all its energy and finally coming to rest. The beta particle has a limited penetrating ability. Its typical range in air is up to about 3 metres. In human tissue, the same beta particle would travel only a few millimetres. Relatively thin layers of plastic, glass, aluminium, or wood easily shield beta particles. Dense materials such as lead should be avoided when shielding beta radiation due to the increase in production of x-rays in the shield. Externally, beta particles are potentially hazardous to the skin and eyes. They cannot penetrate to deep tissue such as the bone marrow or other internal organs. We call this type of external exposure shallow dose. When taken into the body, materials that emit beta radiation can be a hazard in a similar way to that described from alpha emitters - although comparatively less damage is done in the tissue exposed to the beta emitter.

There are two types of beta decay: beta minus and beta plus decay. In beta minus decay a neutron decays into a proton and an electron. The proton stays in the nucleus and the electron is ejected. In beta plus decay, a proton decays into a neutron and a positron which is the anti-particle of the electron. The proton stays in the nucleus and the positron is ejected.

Discovery of the Neutrino

Beta plus decay of proactinium-230 into uranium-230, a positron
and a neutrino.

The neutrino was first postulated in 1930 by Wolfgang Pauli to preserve the laws conservation of energy and momentum in beta decay. He theorized that an undetected particle was carrying away the observed difference between the energy and momentum of the initial and final particles in beta decay. Pauli originally named his proposed light particle a neutron. When James Chadwick discovered a much more massive nuclear particle in 1932 and also named it a neutron, this left the two particles with the same name. Enrico Fermi, who developed the theory of beta decay, coined the term neutrino in 1934 as a way to resolve the confusion. It is the Italian equivalent of "little neutral one".

The process of beta decay seemed to contradict the conservation laws (especially those of energy, linear momentum, and angular momentum). To account for these discrepancies, Pauli proposed the existence of a new particle, the neutrino. The neutrino has no electric charge and no mass, but is able to possess both energy and momentum.

The range of kinetic energies of beta particles emitted during
beta decay. The sum of kinetic energies of the neutrino and
the beta particle represent the energy lost by the nucleus.

During decay it was found that beta particles could have a range of kinetic energies rather than one specific energy as in alpha decay. It was proposed that the total energy lost by the nucleus during decay was shared by the neutrino and the electron being ejected. Since the kinetic energy of the electron varied, there must be another particle whose kinetic energy could also vary so that the sum of their energies was always the same. The simultaneous emission of a beta particle and a neutrino in beta decay allowed for energy and momentum to be conserved. This theory was accepted for almost a quarter of a century without any direct evidence to support it. In 1956, an experiment was performed in a nuclear reactor that could only occur if the neutrino actually existed, thus confirming its existence.

Gamma Decay

Gamma decay of plutonium-240.

Gamma radiation is an electromagnetic wave or photon and has no electrical charge. These photons have no mass but can ionise matter as a result of direct interactions with valence electrons. Like all electromagnetic radiation, gamma rays travel at the speed of light. Because gamma radiation has no charge and no mass, it has a very high penetrating power (said another way, the radiation has a low probability of interacting with matter). Gamma rays have no specific "range" but are characterised by their probability of interacting in a given material. There is no distinct maximum range in matter, but the average range in a given material can be used to compare materials for their shielding ability. Very dense materials, such as lead, concrete, or steel, best shield gamma radiation. Shielding is often expressed by thickness that provides a certain shielding factor, such as a "half-value layer" (HVL). An HVL is the thickness of a given material required to reduce the dose rate to one half the unshielded dose rate.

Due to the high penetrating power, gamma radiation can result in radiation exposure to the whole body rather than a small area of tissue near the source. Therefore, a photon radiation has the same ability to cause dose to tissue whether the source is inside or outside the body. This is in contrast to alpha radiation for example which must be received internally to be a hazard.

When we talk about the gamma decay high-energy electromagnetic waves are emitted from the atomic nucleus. These waves are better known as photons. A gamma decay can happen after an alpha decay or a beta decay, because the atomic nucleus is very energetic. Most alpha decay is also accompanied by subsequent gamma decay.

Decay Series

The radioactive decays series for uranium-238. The last isotope
(lead-206) signifies the end of the series because it is stable.

Radioactivity involves the emission of particles from the nuclei and causes transmutation. In the case of gamma emission, the nucleus remaining will be of the same chemical element, but for alpha, beta, and other radioactive processes, the nucleus will be transmuted into the nucleus of another chemical element. Each decay path will have a characteristic half-life, but some radioisotopes have more than one competing decay path. The half-life of a radioisotope is the time taken for half of a sample to decay into another element.

Naturally occurring uranium is a mixture of three isotopes. The most abundant (greater than 99%) and most stable is uranium-238 (half-life 4.5 x 109 years); also present are uranium-235 (half-life 7 x 108 years) and uranium-234 (half-life 2.5 x 105 years). There are 16 other known isotopes of uranium. Uranium-238 is the parent substance of the 18-member radioactive decay series known as the uranium series. Some relatively long-lived members of this series include uranium-234, thorium-230, and radium-226; the final stable member of the series is lead-206. The decay series is shown in the diagram on the right. The red diagonal arrows represent alpha decay while the blue horizontal arrows represent beta decay.

Mr. Andersen from Bozeman Science explains why radiation occurs and describes the major types of radiation.
He also shows how alpha, beta, and gamma radiation affect the nucleus of a radioactive atom.


Medical and Industrial Radioisotopes

Some medical, industrial and agricultural uses of radioisotopes are summarised below. Some of these isotopes are made in nuclear reactors and some in particle accelerators. Despite the source, each of the examples below utilises the radiation produced in radioactive decay to carry out the function outlined.

Regulating the thickness of paper using the beta emitter

Regulating Paper Thickness
Paper passes between rollers. Beta particles are allowed to pass through the thickness of the paper. If the paper is too thick, few beta particles get through to the detector and the control unit closes the gap in rollers slightly. If it is too thin, too many particles bet through and the gap is increased between the rollers.

A plant's uptake of fertiliser from roots to leaves can be achieved by addition of radioactive tracers to the soil water. Phosphorous-32 is used in agriculture fro this purpose as it has a half-live of 14.3 days and emits beta particles.

Cancer Treatment
Gamma radiation, which can penetrate deep into living tissue from the decay of cobalt-60 can be used to kill cancer cells in a tumour. Colbalt-60 has a half-life of 5.27 years emitting both gamma radiation and beta particles.

Carbon Dating
Living organisms are partly made from carbon, which is recycled through their bodies and the atmosphere as they obtain food and respire. A small portion is the radioactive form carbon-14 (with a half-life of 5730 years). When an organism dies no new carbon-14 is taken into the body and the proportion present gradually falls due to radioactive decay. By measuring the activity, the age of the remains can be used to date organic material (including wood and cloth).

Smoke Detection
These contain a tiny source of α particles which ionise air so that it conducts a current. Smoke entering this chamber attracts ions and reduces the current flowing. This is sensed by a circuit which triggers an alarm. Dating Rocks When rocks are formed some radioisotopes are trapped. As decay continues the proportion of potassium-40 decreases and that of argon-40 increases. The age of rocks can be estimated from the number of half-lives having elapsed.

Detection of Cracks in Metals
Cracks can be detected from photographs using gamma radiation. Gamma sources are compact and do not require an electrical power source (hence are portable). Cobalt-60 is used for this purpose having a half life of 5.27 years and emitting both γ radiation and β particles.

Medical Diagnostic Testing
Iodine-131 is used in nuclear medicine in studying the thyroid gland, having a short half-life of 8.2 days and emitting both gamma radiation and beta particles. A typical example of a diagnostic radioisotope is technetium-99m. This metastable (or excited) form of the Tc-99 isotope has a half-life of only a few hours and decays to stable Tc-99 via gamma ray emission. Hospitals are sent Tc-99m generators, consisting of the molybdenum-99 isotope, which decays with a half-life of 67 hours to Tc-99m. The Tc-99m so obtained is then injected into the body and used to scan for brain, bone, liver, spleen, kidney or lung cancer, as well as for blood flow anomalies. As the Tc-99m de-excites to Tc-99, the emitted gamma radiation is recorded and measured using a gamma ray camera.