The most stable arrangement of nucleons within a nucleus is the one that yields the lowest nuclear energy potential. Radioactive nuclei are those which are not in that lowest arrangement and undergo some change to achieve it. We will look at several types of transformations that enable unstable nuclei to achieve more stability. We refer to that process as radioactive decay.

ALPHA DECAY

A nucleus that contains many protons experiences a large repulsive electromagnetic force. For some nuclei, the attractions exerted by the strong force are not enough to hold the nucleus together. Through a process called alpha decay, a particle containing two protons and two neutrons is ejected from the nucleus. This reduces the repulsive electromagnetic force and makes the whole system more stable. Since the alpha particle has two protons, it is the same as the nucleus of a helium atom. This nucleus is very stable and has a low nuclear potential energy.

In the animation below, a uranium-238 nucleus decays into a thorium-234 nucleus plus an alpha particle. This decay was the source of alpha particles used by Ernest Rutherford and his assistants in the experiment that led them to understand the nuclear atom.

Exercise: Thorium is a radioactive element found in many minerals in the earth's crust. It decays via an alpha decay process. Complete the reaction and account for the nucleons and charge by filling in the table below. For nuclei use the format given the parent, ²³²Th, and type the name(s) of the particles. For the row indicating "number of charges," we are only concerned with the charge of the nuclei and the charge of the ejected particles. Ignore the electrons in the atoms. Place your answers left of the dotted lines.

GAMMA DECAY

When a nucleus is formed in a star, in a nuclear reaction or, or as the daughter in radioactive decay, its neutrons and protons may not be in the lowest energy states allowed by the strong force. When one or more of these nucleons jumps to a lower energy state the excess energy, equivalent to the difference between the higher and lower energy state, is emitted as a gamma ray. A gamma ray is just a photon of electromagnetic radiation.

Gamma ray frequencies are very large because of the large energy separation between nuclear states. High energy gamma rays emitted following the radioactive decay of the nucleus cobalt-60 are used in the treatment of cancer, the sterilization of medical instruments, and the preservation of foods. Cobalt-60 decays by beta emission (be to studied below) to nickel-60 in an excited state. Nickel-60 then decays by two steps to its most stable state by the emission of two high energy gamma rays as is illustrated in the following animation.

Exercise: Cesium-137 is a radioactive element that, like cobalt, is used for medical treatment by gamma irradiation. Cesium-137 decays to a radioactive form of barium-137, which decays by gamma decay to its stable ground state. Complete the reaction for barium-137 and account for the nucleons and charge by filling in the table below. For nuclei use the format given the parent, ¹³⁷Ba, and type the name(s) of the particles. For the row indicating "number of charges," we are only concerned with the charge of the nuclei and the charge of the ejected particles. Ignore the electrons in the atoms. Place your answers left of the dotted lines.

BETA DECAY (electron emission)

When a nucleus is formed initially in a star, in a nuclear reaction, or as the daughter in radioactive decay, its neutrons and protons may not be in the lowest energy state allowed by the strong and electromagnetic forces. Sometimes, the nucleus can be in a lower energy state if one neutron could be changed into a proton. Through the action of the weak force, a neutron can be converted into a proton. During the process, an electron and an anti-electron neutrino are also created; these are emitted from the nucleus.

Later, we will see that Carbon-14 which decays via this process has some important applications.

Exercise: Tritium, or hydrogen-3, is a radioactive nucleus that undergoes beta decay. It is often used as a radioactive tracer in biochemistry research. Complete the reaction for beta decay of hydrogen-3. Account for the nucleons and charge by filling in the table below. For nuclei use the format given for the parent, ³H. You may use e for an electron and neu for a neutrino. For the row indicating "number of charges," we are only concerned with the charge of the nuclei and the charge of the ejected particles. Ignore the electrons in the atoms. Place your answers left of the dotted lines.

POSITRON EMISSION

Some unstable nuclei can become more stable by changing one proton into a neutron. Through the action of the weak force a positively charged electron, called a positron, and a neutrino are created and emitted from the nucleus during this process. The daughter nucleus has an atomic number one lower than the parent nucleus and is more stable then the parent. The positron is a particle of anti-matter, in fact it is an anti-electron, and it can not exist for long in a world of regular matter. It is quickly annihilated by interaction with an electron, and the energy associated with the rest mass of the two particles is coverted to gamma rays. Usually two gamma rays each with 0.511 MeV of energy race apart in opposite directions, as is illustrated in the following animation.

Text to Students for Animation: Fluorine 18 may be created by a nuclear reaction and lives only a short time before it decays by positron emission as is illustrated in the following animation.

Exercise: Carbon-11 beta decays by positron emission, and is often used in medical research. Complete the reaction for positron decay of carbon-11 and account for the nucleons and charge by filling in the table below. For nuclei use the format given the parent, ¹¹C. You may use e for an electron and neu for a neutrino. For the row indicating "number of charges," we are only concerned with the charge of the nuclei and the charge of the ejected particles. Ignore the electrons in the atoms. Place your answers to the left of the dotted lines.

ELECTRON CAPTURE

When a nucleus is formed in a star, in a nuclear reaction, or as the daughter in radioactive decay, a combination of the strong force and the electromagnetic force may allow the neutrons and protons to be in a lower energy state if a one proton is changed into a neutron. Through the action of the weak force, an electron from one of the inner most electron orbitals surrounding the nucleus is combined with a proton and a neutrino is emitted from the nucleus. This process converts a proton into a neutron. The daughter nucleus has an atomic number one lower than the parent nucleus and is more stable then the parent.

Potassium-40 is found in all natural potassium samples. About eleven percent of potassium-40 atoms decay via an electron capture process. Because the process occurs very slowly, it is useful as a tool in studying the age of rocks, as we will see later.

The electron capture process is illustrated in the following animation.

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Exercise: Beryllium-7 decays by electron capture beta decay. This process is of importance during the formation of elements in stars. Complete this reaction for the electron capture of beryllium-7 and account for the nucleons and charge by filling in the table below. For nuclei use the format given the parent, ⁷Be. You may use e for an electron and neu for a neutrino. For the row indicating "number of charges," we are only concerned with the charge of the nuclei and the charge of the ejected particles. Ignore the electrons in the atoms. Place your answers left of the dotted lines.

A nucleus that contains many protons has a large repulsive electromagnetic force in the nucleus. For some nuclei, the strong attractive nuclear force can not hold the nucleus together. Some such nuclei decay by emission of an alpha particle as noted earlier. Other heavy nuclei split into nearly equal daughters plus one or two neutrons. This decay is called fission. The two smaller nuclei have less repulsive electromagnetic force and are more stable. However, they usually have too many neutrons and go through several steps of beta decay until the nuclei are stable.

In the animation below a uranium-238 nucleus decays into two fission products plus some neutrons. As we will see later, this natural fission decay is used to provide the neutrons which initiate the induced fission chain reaction employed in many nuclear power plants.

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Exercise: Californium-252 is a man-made radioactive element. It is generated by placing uranium-238 in a nuclear reactor where it absorbs a neutron then decays by beta emission to the next higher element. This cycle is repeated several times to produce californium. Complete the reaction for fission decay of californium-252 that is given in part below. Account for the nucleons and charge by filling in the table. For nuclei use the format given by the parent, ²⁵²Cf. For the row indicating "number of charges," we are only concerned with the charge of the nuclei and the charge of the ejected particles. Ignore the electrons in the atoms. Place your answers left of the dotted lines.