Dating using half-lives

SAMPLE PROBLEM 16.7 Dating Using Half-Lives... 

A new Sample Problem, Dating Using Half-Lives, now calculates time elapsed for a bone sample. 

The radioactive isotope carbon-14 is used for radiocarbon dating. The half-life of carbon-14 is 5.73 X 10 years. A wooden artifact in a museum has a to ratio that is 0.775 times that found in living organisms. Estimate the age of the artifact. 

Carbon has seven isotopes. In 1961 the International Union of Pure and Applied Chemistry adopted the isotope carbon-12 as the basis for atomic weights. Carbon-14, an isotope with a half-life of 5715 years, has been widely used to date such materials as wood, archaeological specimens, etc. 

Rhenium, atomic wt 186.2, occurs in nature as two nucHdes Re [14391-28-7] mass 184.9530, in 37.500% abundance and Re [14391-29-8], mass 186.9560, in 62.500% abundance. The latter isotope is radioactive, emitting very low energy radiation and having a half-life estimated at 4.3 ( 0.5) X 10 ° yr. The radioactive decay of this isotope has been used to date accurately the time of Earth s formation. 

The effects of leukotrienes can be blocked at several levels. Inhibitors of FLAP or 5-LO inhibit LT synthesis at all levels. However, FLAP antagonists developed to date have been too hepatotoxic for human use. Zileuton, a 5-LO synthase inhibiting drug, also demonstrated some hepatotoxicity in a small percentage of patients, which was nonetheless entirely reversible. However, the short half-life of this compound requires four times daily... 

The constant half-life of a nuclide is used to determine the ages of archaeological artifacts. In isotopic dating, we measure the activity of the radioactive isotopes that they contain. Isotopes used for dating objects include uranium-238, potassium-40, and tritium. However, the most important example is radiocarbon dating, which uses the decay of carbon-14, for which the half-life is 5730 a. 

These isotopes are sometimes used as tracers of natural terrestrial processes and cycles. Long-lived isotopes, such as Rb and Sm are used for precise dating of geological samples. When the solar system formed it also contained several short-lived isotopes that have since decayed and are now extinct in natural systems. These include Al, Fe, Pu, Pd, and Al with a half-life of less than a million years is particularly important because it is a potentially powerful heat source for planetary bodies and because its existence in the early solar system places tight constraints on the early solar system chronology. 

Most CO and CO2 in the atmosphere contain the mass 12 isotope of carbon. However, due to the reaction of cosmic ray neutrons with nitrogen in the upper atmosphere, C is produced. Nuclear bomb explosions also produce C. The C is oxidized, first to CO and then to C02 by OH- radicals. As a result, all CO2 in the atmosphere contains some 0, currently a fraction of ca. 10 of all CO2. Since C is radioactive (j -emitter, 0.156 MeV, half-life of 5770 years), all atmospheric CO2 is slightly radioactive. Again, since atmospheric CO2 is the carbon source for photos5mthesis, aU biomass contains C and its level of radioactivity can be used to date the age of the biological material. 

Exponential decay is quite regular starting with a given amount of a substance at t = 0, this amount will fall to V2 its original value after one half-life, to 1/4 after two half-lives, Vs after three half-lives, and so forth. This regularity has its usefulness, and the decay of has been widely employed to date archeological artifacts [3]. 

One other highly useful chronometer is measurement of °Po- b disequilibria. °Po has a half-life of 138.4 days making the chronometer active for 2 yrs. °Po- °Pb fractionation is based on Po but not Pb partitioning into volatiles during degassing (Gill et al. 1985). Ey repeat analysis of °Po, Rubin et al. (1994) constrained the time of eruption of several samples from 9°N EPR to windows of-100 days. These dates are consistent with eruption windows based on submersible observation. Thus, this technique can provide critical age constraints for other U-series parent-daughter pairs but requires that samples be collected and analyzed as soon as possible after eruption. 

Ra is soluble and therefore tends to be released to deep waters when it is formed by °Th decay in marine sediments. Substrates which capture the resulting excess of Ra found in seawater can potentially be dated using the decay of this Ra excess ( Raxs). Unfortunately there is no stable isotope of Ra with which to normalize measured Ra values but the marine chemistry of Ba is sufficiently close to that of Ra that it can be used as a surrogate for a stable Ra isotope and seawater Ra/Ba ratios are constant throughout the oceans, except in the deep North Pacific (Chan et al. 1976). The half life of Ra is only 1600 years so Raxs/Ba chronology is limited to the Holocene but it nevertheless has potential for use in several regions. 

Comparing and Contrasting 14C decays to 14N with a half-life of 5730 years. This reaction is used for radiochemical dating of a certain class of terrestrial objects. How many half-lives of 40C have passed since the Zag meteorite formed ... 

Lenalidomide was approved recently for the indication of myelodysplastic syndrome where the 5q deletion is present. Since lenalidomide is an analog of thalidomide, all the same precautions must be taken to prevent phocomelia. The time to maximum lenalidomide concentrations occurs 0.5 to 4 hours after the dose. The terminal half-life ranges from 3 to 9 hours. Approximately 65% of lenalidomide is eliminated unchanged in the urine, with clearance exceeding the glomerular filtration rate. To date, no pharmacokinetic studies have been done in patients with renal dysfunction. Lenalidomide is used in the treatment of myelodysplastic syndrome and multiple myeloma. Other side effects are neutropenia, thrombocytopenia, deep vein thrombosis, and pulmonary embolus. 

The half-life of radiocarbon used to calculate radiocarbon dates is 5568 years, a value known to be about 3% in error with respect to the actual half-life of radiocarbon, 5730 years. This is done to avoid confusion... 

The half-life is independent of the initial number of nuclei. For 14C decay the half-life is 5717 years, whereas the 238U decay half-life is 4.5 billion years. Carbon dating works well for timescales in the recent past and is used for dating objects such as the Turin shroud, but 238U is better for timescales of the age of the solar system. 

For more recent dating processes carbon dating is used. With a half-life of 5717 years 14C dating relies on the replenishment of the 14C parent species, which occurs by neutron capture. The process occurs in the atmosphere as a result of bombardment of the Earth with neutrons ... 

This technique is useful only when dating objects that are less than 50,000 years old (roughly 10 times the half-life of carbon-14). Older objects have too little activity to be accurately dated. This technique depends on cosmic-ray intensity being constant or at least predictable in order to keep the 14C/12C known throughout the time interval. Also, the sample must not be contaminated with organic matter having a different 14C/12C ratio. 

We were quite elated, and it appeared that it was a rich field. Now, fifty years later, I must say that it wasn t as rich as we thought. But we have over the years discovered half a dozen natural radioactive elements, and two of these, the samarium-147 with its decay to neodymium-143 and rhenium-187 with its decay to osmium-187, prove to be of use in Nuclear Dating. The importance of rhenium is that it is iron soluble while the other radioactivities are insoluble in metallic iron. In fact, the best half life we have for rhenium-187 was obtained by measuring the osmium-187 to rhenium-187 ratio in iron meteorites which had been dated by other methods. This work was started many years ago by Dr. Herr and others in Germany. The half life is 43,000,000,000 years. 

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