Concept explainers
Interpretation:
Age of the charcoal has to be calculated.
Concept Introduction:
For a radioactive isotope, the relative instability is expressed in terms of half-life. Half-life is the time required for half of the given quantity of the radioisotope to undergo radioactive decay. Half-life of the radioactive isotope is independent of the quantity of the radioactive isotope. Half-life of a radioactive isotope can be expressed as,
Number of disintegrations per unit time is known as the activity of the sample. The rate of radioactive decay can be expressed as,
Where,
If initial activity of the sample is
Rearranging equation (3) as shown below,
Considering equation (2), the equation (3) can be rewritten in terms of fraction of radioactive atoms that is present after time
Explanation of Solution
Mass of carbon present in
Half-life of carbon-14 is
Disintegration rate of carbon-14 is given as
The initial activity (
Age of the charcoal can be calculated as shown below,
Therefore, the age of the charcoal is estimated to be
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Chapter 18 Solutions
Chemistry: The Molecular Science
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