Scientists can determine the age of ancient objects by the method of radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, ¹4C, with a half-life of about5,730 years. Vegetation absorbs carbon dioxide through the atmosphere, and animal life assimilates ¹4C through food chains. When a plant or animal dies, it stops replacing its carbon, and the amount of ¹4C present begins to decreasethrough radioactive decay. Therefore, the level of radioactivity must also decay exponentially.A discovery revealed a parchment fragment that had about 54% as much 14C radioactivity as does plant material on the earth today. Estimate the age (in years) of the parchment. (Round your answer to the nearest hundred years.)

The half-life of the isotope is 5730 yrs.To Find:Estimate the age of the parchment.

Answered: Scientists can determine the age of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A radioactive substance has a half life of 175 years. Find the decay constant, r, for this substance. (Round to 5 places after the decimal point.)
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Element X decays radioactively with a half life of 9 minutes. If there are 170 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 26 grams?
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Suppose a radioactive substance has a half-life of 1000 years. What fraction will be leftafter 1000 years?
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In 1986 the Chernobyl nuclear power plant exploded, and scattered radioactive material over Europe. Of particular note were the two radioactive elements iodine-131 whose half-life is 8 days and cesium-137 whose half-life is 30 years. How much of cesium-137 remains in the area to this date (2021)?
Mikey and his gang of friends find a map leading to a treasure owned by a pirate living in the 17th century. To authenticate the map, Mikey carbon-dates the map by measuring the amount of carbon-14 currently in the map relative to the amount originally present when the map was drawn and finds that 96% of the carbon-14 is still present. If the half-life of carbon-14 is 5730 years, how long ago was the map drawn up? Round to the nearest year. Does the age of the map support its authenticity?
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A wooden artifact from an ancient tomb contains 50 percent of the carbon-14 that is present in living trees.How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.) ________ years
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