Since nuclear decay follows first-order kinetics, we can adapt the mathematical relationships used for first-order chemical reactions. We generally substitute the number of nuclei, N , for the concentration. If the rate is stated in nuclear decays per second, we refer to it as the activity of the radioactive sample. The rate for radioactive decay is:. Example 1 applies these calculations to find the rates of radioactive decay for specific nuclides.
How long will it take a sample of radon with a mass of 0. Because each nuclide has a specific number of nucleons, a particular balance of repulsion and attraction, and its own degree of stability, the half-lives of radioactive nuclides vary widely. The half-lives of a number of radioactive isotopes important to medicine are shown in Table 1, and others are listed in Half-Lives for Several Radioactive Isotopes.
This process is radiometric dating and has been responsible for many breakthrough scientific discoveries about the geological history of the earth, the evolution of life, and the history of human civilization. We will explore some of the most common types of radioactive dating and how the particular isotopes work for each type.
The radioactivity of carbon provides a method for dating objects that were a part of a living organism. This method of radiometric dating, which is also called radiocarbon dating or carbon dating, is accurate for dating carbon-containing substances that are up to about 30, years old, and can provide reasonably accurate dates up to a maximum of about 50, years old. Carbon forms in the upper atmosphere by the reaction of nitrogen atoms with neutrons from cosmic rays in space:.
All isotopes of carbon react with oxygen to produce CO 2 molecules. But when the plant dies, it no longer traps carbon through photosynthesis. The decrease in the ratio with time provides a measure of the time that has elapsed since the death of the plant or other organism that ate the plant. Figure 7 visually depicts this process. Figure 7. Along with stable carbon, radioactive carbon is taken in by plants and animals, and remains at a constant level within them while they are alive.
After death, the C decays and the CC ratio in the remains decreases. Comparing this ratio to the CC ratio in living organisms allows us to determine how long ago the organism lived and died. A tiny piece of paper produced from formerly living plant matter taken from the Dead Sea Scrolls has an activity of If the initial C activity was Figure 8. Carbon dating has shown that these pages from the Dead Sea Scrolls were written or copied on paper made from plants that died between BCE and CE More accurate dates of the reigns of ancient Egyptian pharaohs have been determined recently using plants that were preserved in their tombs.
Fortunately, however, we can use other data, such as tree dating via examination of annual growth rings, to calculate correction factors. With these correction factors, accurate dates can be determined. In general, radioactive dating only works for about 10 half-lives; therefore, the limit for carbon dating is about 57, years. Radioactive dating can also use other radioactive nuclides with longer half-lives to date older events. For example, uranium which decays in a series of steps into lead can be used for establishing the age of rocks and the approximate age of the oldest rocks on earth.
Since U has a half-life of 4. In a sample of rock that does not contain appreciable amounts of Pb, the most abundant isotope of lead, we can assume that lead was not present when the rock was formed.
Therefore, by measuring and analyzing the ratio of UPb, we can determine the age of the rock. This assumes that all of the lead present came from the decay of uranium If there is additional lead present, which is indicated by the presence of other lead isotopes in the sample, it is necessary to make an adjustment. Potassium-argon dating uses a similar method. K decays by positron emission and electron capture to form Ar with a half-life of 1. If a rock sample is crushed and the amount of Ar gas that escapes is measured, determination of the ArK ratio yields the age of the rock.
Other methods, such as rubidium-strontium dating Rb decays into Sr with a half-life of As of , the oldest known rocks on earth are the Jack Hills zircons from Australia, found by uranium-lead dating to be almost 4.
An igneous rock contains 9. Determine the approximate time at which the rock formed. The sample of rock contains very little Pb, the most common isotope of lead, so we can safely assume that all the Pb in the rock was produced by the radioactive decay of U When the rock formed, it contained all of the U currently in it, plus some U that has since undergone radioactive decay.
Elements in the periodic table can take on several forms. Some of these forms are stable; other forms are unstable. Typically, the most stable form of an element is the most common in nature. However, all elements have an unstable form. Unstable forms emit ionizing radiation and are radioactive. There are some elements with no stable form that are always radioactive, such as uranium.
Elements that emit ionizing radiation are called radionuclides. When it decays, a radionuclide transforms into a different atom - a decay product. The atoms keep transforming to new decay products until they reach a stable state and are no longer radioactive. The majority of radionuclides only decay once before becoming stable.
When the ratio of neutrons to protons in the nucleus is too low, certain atoms restore the balance by emitting alpha particles. They are relatively heavy, high-energy particles that cannot penetrate most matter.
A piece of paper or the dead outer layers of skin is sufficient to stop alpha particles. Radioactive material that emits alpha particles alpha emitters can be very harmful when inhaled, swallowed or absorbed into the blood stream because internal organs are more directly exposed without a protective layer of skin cells.
Image of a beta particle. Beta particle emission occurs when the ratio of neutrons to protons in the nucleus is too high.
In this case, an excess neutron transforms into a proton and an electron. The proton stays in the nucleus and the electron -1 is ejected energetically. This process decreases the number of neutrons by one and increases the number of protons by one.
Since the number of protons in the nucleus of an atom determines the element, the conversion of a neutron to a proton actually changes the radioactive element radionuclide to a different element. The speed of individual beta particles depends on how much energy they have, and varies widely. Beta particles can be stopped by a layer or two of clothing or by a few millimeters of a substance such as aluminum.
They are capable of penetrating the skin and causing radiation damage, such as skin burns. As with alpha emitters, beta emitters are most hazardous when they are inhaled or ingested. Image of a gamma ray. Gamma radiation is very high-energy ionizing radiation.
Gamma rays have no mass and no electrical charge — they are pure electromagnetic energy. Gamma rays travel at the speed of light and can cover hundreds to thousands of meters through the air before expending their energy.
They can easily penetrate barriers such as skin and clothing. Gamma rays have so much penetrating power that several inches of a dense material like lead or several feet of concrete may be required to stop them.
The RadTown Radioactive Atom activities are designed to help middle and high school students identify the structure of an atom and describe the structural changes that occur in unstable radioactive atoms as they decay. Students will also learn about the process of radioactive decay and the types of ionizing radiation emitted from radioactive atoms as they decay.
Additionally, students will learn about commonly encountered radioactive elements, fission and fusion. Regardless of where the residual ion of an alpha decay event ends up it will achieve electrical neutrality and reside as a foreigner among its neighboring atoms. The other decay modes will not be discussed here as most of the major considerations that apply to your question are covered by the cases considered above. There are some additional implications of the process of atom identity change and displacement that are important in specialized situations but they are beyond the intended scope of this discussion.
George Chabot, PhD. The information posted on this web page is intended as general reference information only. Specific facts and circumstances may affect the applicability of concepts, materials, and information described herein. The information provided is not a substitute for professional advice and should not be relied upon in the absence of such professional advice. To the best of our knowledge, answers are correct at the time they are posted.
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