Half-life of carbon

A sample of a wooden artifact gives 5.0 disintegrations/min/g carbon. The half-life of carbon-14 is 5730 years, and the activity of C-14 in wood just cut down from a tree is 15.3 disintegrations/min/g carbon. How old is the wooden artifact ... 

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. 

Calculate the rate constant, k, from the half-life of carbon-11. 

The evaporation half-life of carbon tetrachloride (1 mg/L) from water at 25 °C using a shallow-pitch propeller stirrer at 200 rpm at an average depth of 6.5 cm was 29 min (Dilling et al., 1977). 

The concentration of carbon tetrachloride appeared to decline exponentially in a biphasic manner, with an initial half-life of less than 1 hour, and a second-phase half-life of about 40 hours. Roughly similar results were observed in several volunteers who breathed carbon tetrachloride for 1-3 hours, where the half-life of carbon tetrachloride in expired air over the first several hour period after exposure was less than 1 hour (Stewart et al. 1961). 

The concentration of carbon tetrachloride was measured in the expired air of a person who swallowed a large amount of carbon tetrachloride (Stewart et al. 1963). Excretion in expired air was found to decrease exponentially in a biphasic or multiphasic fashion, but no quantitative estimate of the elimination half-life of carbon tetrachloride or of the fraction of the dose excreted by this pathway was provided. Visual inspection of their graphed data suggests very approximate half-lives of less than several hours initially, 40 hours (75-150 hours post exposure), and 85 hours (300-400 hours post exposure). 

No studies were located on the degradation of carbon tetrachloride in soil or sediment. Based on the estimated aqueous aerobic biodegradation half-life of carbon tetrachloride the half-life of carbon tetrachloride in soil is estimated to be 6-12 months (Howard et al. 1991). 

The answer, 5,714 years, closely matches the half-life of carbon-14 in Table 20-1. (Try to keep the numbers in your calculator throughout each step of the process, and don t round until the end of the problem.)... 

The half-life of carbon-14 is 5,730 years. This means that in a given sample of carbon-14, half the atoms will decay in 5,730 years. During the next 5,730 years, half the remaining atoms will decay. This continues until there are no carbon-14 atoms left. 

The half-life of carbon-14 is about 5730 years. This means that half of the carbon-14 atoms now present in a plant or animal that dies today will decay in the next 5730 years. Half of the remaining carbon-14 atoms will then decay in the following 5730 years, and so on. 

Radioactive decay rates are statistical averages of large numbers of decaying atoms. Because of the relatively short half-life of carbon-14, only trace amounts would be left after 50,000 years—too little to be statistically accurate. 

The Dead Sea scrolls were found hy radioactive carbon-dating techniques to have 11.9 cpm per gram of carbon. Living material similar to that from which they were made has 15.3 cpm per gram of carbon. How old must the scrolls be, knowing that the half-life of carbon-14 is 5730 yr ... 

PROBLEM 22.4 The half-life of carbon-14 is 5730 years. What is its decay constant ... 

The half-life of carbon-14 is about 5,500 years so that no corrections are needed for decay during the course of experiments. In materials of very high specific activity, there is the possibility of significant amounts of radiolysis brought about by the /5-radiations. 

Carbon-14 is a natural isotope of carbon. It is also a radioisotope, which means that it is radioactive. Radioisotopes break down, or decay, in a specific amount of time. The amount of time it takes for half of the atoms of a radioisotope to decay is called its half-life The half-life of carbon-14 is about 5,700 years. 

The age of an art object can provide a valuable clue to whether it is real or a forgery. Because the half-life for a specific isotope is constant, half-life can be used to find the age of an object. The isotope put to use for radioactive dating is carbon-14. The half-life of carbon-14 is 5,730 years. The amount of carbon-14 in our atmosphere remains fairly constant. When an object such as a plant is alive, it absorbs C02. The carbon atoms in the C02 are made of a specific ratio of carbon-14 atoms to carbon-12 atoms. The carbon-14 atoms decay by emission of beta particles ... 

If you were able to observe a single atom of carbon-14, you would know that it would eventually decay, but there would be no way of knowing exactly when it would happen. If you take billions of carbon-14 atoms, you can say nothing about when any individual nucleus will emit radiation, but you can say that after 5770 years half of them will have broken down. This is what is called the half-life of carbon-14. Different radioactive isotopes have different half-lives. The half-life of uranium-238, for example , is 4.5 billion years, and that of uranium-235 is 710 million years. 

Table 2 shows that the half-life of carbon-14 is 5715 years. After that interval, only half of the original amount of carbon-14 will remain. In another 5715 years, half of the remaining carbon-14 atoms will have decayed and leave one-fourth of the original amount. 

To find the age of the artifact, multiply the half-life of carbon-14 three times for the three half-lives that have elapsed. 

When you perform calculations, such as using half-life of carbon to determine the age of the skull in Figure 22 or the pH of the products in Figure 23, you may need to use the log or antilog function on your calculator. A logarithm (log) is the power or exponent to which a number, called a base, must be raised in order to obtain a given positive number. This textbook uses common logarithms based on a base of 10. Therefore, the common log of any number is the power to which ten is raised to equal that number. Examine Table 4. Note the log of each number is the power of ten for the exponent of that number. For example, the common log of 100 is two and the common log of 0.01 is -2. 

Carbon tetrachloride is highly volatile and is relatively stable in the environment. Therefore, nearly all of the carbon tetrachloride produced is eventually emitted to the atmosphere. The chemical moves readily through soil and adsorbs only slightly to sediment. The estimated half-life of carbon tetrachloride in the atmosphere is 30-100 years. The hydrolysis half-life in water is estimated to be 7000 years at 25°C. Carbon tetrachloride has a low potential to bioconcentrate in animals. The logarithm of the bioconcentration factor in trout is 1.24. 

A piece of wood taken from a cave dwelling in New Mexico is found to have a carbon-14 activity (per gram of carbon) only 0.636 times that of wood cut today. Estimate the age of the wood. The half-life of carbon-14 is 5730 years. 

A skeleton was found in the woods and the poUce would like to place the approximate time of death. A sample of bone from the skeleton produces 12.0 disintegrations per min per g of C. Bone of recent origin produces 14.0 disintegrations per min per g C. Calculate the approximate age of the bone sample. The half-life of carbon-14 is 5730 years. 

The half-life of carbon-14,5730 years, is short compared with the age of many fossils and geological formations. As a result, objects more than about 60 000 years old cannot be dated using this technique because the amount of carbon-14 left in them is too small to be measured accurately. 

Radiocarbon dating is a process used to determine the age of objects. The ratio of the masses of the stable isotope, carbon-12, and unstable isotope, carbon-14, is measured. Using this value and the half-life of carbon-14, the age of the coffin may be calculated. 

O How do half-lives of tracers compare to the half-life of carbon-14 Why would these nuclides be a better choice for medical applications than carbon-14 ... 

The standard measurement in radioactive decay is called a half-life. This is how long it would take a certain amount of a substance to decay to half its weight (a gram to half a gram, for instance). The half-life of carbon-14 is 5,730 years (plus or minus 40 years). To measure the age of things, scientists make the supposition that the ratio of carbon-12 to carbon-14 in the atmosphere has remained constant over time. 

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