Half-Life
Half-life is a scientific term that describes the time required for half of a given quantity of a material to undergo a process characterized by exponential decay. This concept is most commonly associated with radioactive isotopes, which have unstable atomic nuclei due to an imbalance of protons and neutrons. During radioactive decay, these materials emit subatomic particles and transition towards a more stable state. The process is mathematically expressed through an exponential rate law, allowing for the calculation of the remaining quantity of material over time.
One notable application of half-life is in carbon dating, a method used to determine the age of organic materials by measuring the ratio of carbon-14, a radioactive isotope, to carbon-12. This technique relies on the fact that carbon-14 is continuously incorporated into living organisms but ceases upon their death, leading to a predictable decay pattern. Understanding half-life is crucial not only in fields like archaeology and geology but also in medicine and nuclear physics, where it informs safety standards and the handling of radioactive materials. Ultimately, the half-life concept highlights the natural processes of decay and stability within the universe.
Half-Life
FIELDS OF STUDY: Nuclear Chemistry; Physical Chemistry
ABSTRACT
The half-life describes the condition in an exponential rate process at which one-half of any given amount of material is consumed in the process. The concept is particularly useful in determining the age of a radioactive material.
Half-Life Defined
The term "half-life" refers to the length of time required for one-half of any given amount of a material to be consumed in a process that proceeds according to an exponential rate expression. It is applicable to any and all such processes but is most often used in reference to the process of exponential decay that occurs in radioactive isotopes.
Radioactivity exists when an atomic nucleus contains an unstable combination of protons and neutrons. Because each proton bears a positive electrical charge, a strong force of repulsion exists between protons when more than one is present in a nucleus. The neutron, which is electrically neutral and only very slightly more massive than a proton, seems to have an internal structure that effectively places some negative charge that exists within it next to the adjacent protons, allowing it to function as a sort of nuclear glue to hold the protons together and stabilize the nucleus. There are numbers of protons that cannot be adequately balanced by the presence of any whole-number combination of neutrons. Atomic nuclei with this imbalance, whether due to too many or too few neutrons, are unstable and therefore radioactive.
Radioactive decay is said to be exponential because it obeys the exponential rate law
At = A0e−kt
in which A0 is the amount of material originally present, At is the amount of material present after a specific amount of elapsed time (t), and k is the specific rate constant for the process. The mathematical constant e is known as the natural base, an indeterminate irrational number that has an approximate value of 2.718281828 and is a common feature of the natural world. The exponent −kt is the logarithm of the value At/A0 to the base e, meaning that is the power to which e must be raised in order to equal At/A0. Many may be more familiar with the base-10 use of logarithms, which functions the same way. For example, the logarithm of 100 to base 10 is 2, since 102 = 100. To differentiate the two, the logarithm of base e is commonly called the "natural logarithm," abbreviated ln or loge.
According to the above rate expression, the half-life is the time (t) that has elapsed when At is exactly one-half of the value of A0, or
When the expression is rearranged and substituted into the rate expression, it becomes
The logarithms of both sides of the equation must also be equal. Therefore,
The half-life of the process (t1/2) is thus given by the equation
In physical terms, this means that when the amount of time equal to the half-life of the process has passed, regardless of the value of k, there will be half the amount of non-decayed material that there was at the beginning of the half-life period. When a second half-life’s worth of time has passed, just half of that half—one-quarter of the original amount—will remain. After a third half-life, just one-eighth of the original amount will remain, and so on. The fraction remaining after n half-lives can therefore be expressed as
It should be noted that no matter how many half-lives pass, there will always be some amount of the original material left, until only one atom or molecule of the material remains. When that atom or molecule is consumed, the process ends. In radioactive decay, the process ends when a stable nucleus forms.
History of Radioactivity
Though radioactive materials have existed naturally since the beginning of the universe, formed by various nuclear processes, people did not know about them until it became possible to detect their effects. French physicist Henri Becquerel (1852–1908) first recognized radioactive emanations from uranium ore at the end of the nineteenth century. This led to the isolation and identification of radium and other radioactive elements, notably by husband-and-wife physicists Pierre Curie (1859–1906) and Marie Curie (1867–1934).
Unfortunately for many researchers in this area, the adverse health effects of radiation were unknown at the time, and most researchers lived considerably shorter lives than they would have otherwise. General ignorance of the effects of radiation exposure persisted well into the twentieth century. For example, luminous-dial wristwatches, on which the numbers glowed in the dark due to radioactive radium or promethium in the paint, were popular well into the 1960s; tritium, a radioactive isotope of hydrogen, was used until the mid-1990s. The manufacture of such products was stopped when it was recognized that long-term exposure to even such small amounts of nuclear radiation was unhealthy.
As understanding of nuclear composition and decay processes grew with the development of the modern atomic theory, high-energy physics researchers sought to apply the knowledge to the identification of previously unknown transuranium elements, including those in the actinide series.
Measuring Age by Half-Life
Using the half-life relationship described above and the rates of decay of various isotopes of different elements, one can determine the age of various materials by measuring the ratio of starting materials of a nuclear-decay process to products. Carbon dating is perhaps the best-known application of this technique.
The radioactive isotope carbon-14 is produced by the near-constant collision of cosmic-ray particles with the nuclei of carbon atoms in atmospheric carbon dioxide. The amount of carbon-14 present in the atmosphere is effectively constant, though there have been some small variations over time, as well as more substantial variations due to nuclear testing and the burning of fossil fuels. When a plant incorporates carbon dioxide into glucose during photosynthesis, or when an animal consumes plant matter that has done so, the proportion of carbon-14 to carbon-12 in the living plant or animal’s system also remains constant. However, when the plant or animal dies, incorporation of carbon-14 ceases, and the carbon-14 present in the organic material begins to decrease in proportion. By comparing the ratio of carbon-14 to carbon-12 in a sample with the corresponding ratio in a living system, one can calculate the amount of radioactive decay that has taken place and, from that, the number of carbon-14 half-lives that have passed since the material ceased to incorporate new carbon-14—that is, since it was alive.
PRINCIPAL TERMS
- carbon dating: a method of dating that uses the proportion of radioactive carbon-14 atoms remaining in an organic material to determine the amount of time that has elapsed since it was part of a living organism.
- exponential decay: a process of decomposition in which the amount of non-decayed material decreases at a rate proportional to the current amount of material present rather than the original amount.
- isotope: an atom of a specific element that contains the usual number of protons in its nucleus but a different number of neutrons.
- logarithm: the exponent, or power, to which a specific base number must be raised to produce a given value; commonly abbreviated "log."
- radioactivity: the emission of subatomic particles due to the spontaneous decay of an unstable atomic nucleus, the process ending with the formation of a stable atomic nucleus of lower mass.
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