|MadSci Network: Physics|
Dear Chloe, In phrasing your question, you said "However positron emission only occurs in artificially produced isotopes, rather than naturally occurring radioactive isotopes." This is not true. There is one very important naturally occurring radioactive isotope of potassium, K-40, which decays by positron emission. 0.0117% of all the potassium atoms in the world are this isotope (one out of every 8540 potassium atoms). K-40 is used in the radioactive dating of igneous rocks. See this link for more details: http://id-archserve.ucsb.edu/Anth3/Courseware/Chronology/09_Potassium_Argon_Dating.html It is true, however, that positron emission is rare in naturally occurring radioactive isotopes. A glance through the CRC Handbook of Chemistry and Physics (77th edition) Table of the Isotopes reveals that of the 18 naturally occurring radioactive nuclei with isotopic abundances over 0.01%, only K-40 decays by positron emission; the others decay by emitting alpha particles, beta particles (electrons), or gamma rays, or by capturing electrons. If you will allow me to rephrase your question, let's ask instead, "Why is decay by positron emission such a rare process among naturally occurring radioactive isotopes?" There are three reasons. In beta decay, or electron emission, a neutron is converted into a proton, an electron, and an antineutrino. Symbolically, 0 + - _ n --> p + e + v This reaction can proceed inside or outside the nucleus of an atom, even with free neutrons because the neutron on the left-hand side is more massive than its decay products on the right-hand side, and the excess mass is converted into the kinetic energies of the decay products through Einstein's famous formula E=mc^2. In positron emission, a proton is converted into a neutron, a positron (or antielectron), and a neutrino. Symbolically, + 0 + p --> n + e + v This reaction can NOT proceed outside the nucleus because the proton on the left-hand side is LESS massive than its decay products on the right-hand side. Free protons are stable against this kind of decay. In the nucleus, some of the energy that binds the protons and neutrons together can be used to make the reaction go. REASON #1: Electron emission is energetically favored over positron emission because neutrons are more massive than protons. Most naturally occurring nuclides, especially the heavier isotopes, contain more neutrons than protons. The protons, being positively charged, repel each other through the electric force but they also attract each other through the strong force. Neutrons, being neutral, are not affected by the electric force, but do interact through the strong force. Neutrons supply the "glue" to bind a nucleus together. Neutrons and protons are spin one-half particles (so are electrons) and they obey the Pauli Exclusion Principle: No two spin one-half particles can be in the same place at the same time. Because the neutrons and protons can not exist on top of one another, newly added particles must go into higher and higher energy states. In order for a nucleus to emit a positron, a proton in the nucleus must convert to a neutron. Since there are already a lot of neutrons in the nucleus, it is not likely that the newly created neutron will find an unfilled low-energy state. On the other hand, in order for a nucleus to emit an electron, a neutron must convert to a proton. Since there are not as many protons in the nucleus, chances are good that the newly created proton will find an unoccupied low-energy state. REASON #2: There are more neutrons than protons in most nuclei. The Pauli Exclusion Principle favors changing neutrons into protons by emitting electrons (beta decay) over changing protons into neutrons by positron emission. There is a radioactive decay process called "electron capture" which is always found whenever positron emission occurs. In electron capture, an electron orbiting around the nucleus of an atom sometimes wanders into the nucleus and combines with a proton to produce a neutron and a neutrino. Symbolically, + - 0 p + e --> n + v As in positron emission, this process can only take place inside the nucleus because the left-hand side is less massive than the right-hand side so some energy must be supplied by the nucleus itself to make the reaction go. But this reaction requires LESS energy from the nucleus than positron emission requires. In fact, there are two other naturally occurring radioactive isotopes besides potassium-40 which decay by electron capture: vanadium-50 and tellurium-123. But neither of these isotopes can emit positrons because the nuclei can not supply enough energy to run the reaction. The energy needed is relatively large in the nuclear realm -- twice the rest mass energy of the electron, 1.022 MeV. REASON #3: There is a hurdle or energy threshold to overcome before positron emission is possible. --Dr. Randall J. Scalise http://www.phys.psu.edu/~scalise/
Try the links in the MadSci Library for more information on Physics.