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Chapter 21: Problem 82

The constituents of wine contain, among others, carbon, hydrogen, and oxygen atoms. A bottle of wine was sealed about 6 yr ago. To confirm its age, which of the isotopes would you choose in a radioactive dating study? The half-lives of the isotopes are: \({ }^{14} \mathrm{C}: 5730 \mathrm{yr}\) \({ }^{15} \mathrm{O}: 124 \mathrm{~s} ;{ }^{3} \mathrm{H}: 12.5 \mathrm{yr}\). Assume that the activities of the isotopes were known at the time the bottle was sealed.

Short Answer

Expert verified
The isotope \({ }^{3} \mathrm{H}\) (Tritium) should be chosen for the radioactive dating study as its half-life of 12.5 years is the closest to the 6-year age of the bottle of wine to be confirmed.

Step by step solution

01

Phase 1 - Understanding Isotopes and Half-Lives

Isotopes are versions of elements with differing numbers of neutrons in their nuclei. Radioactive isotopes, or radioisotopes, decay over time releasing radiation. The rate at which they decay is measured in terms of their 'half-life', which is the time taken for half of the radioactive isotopes to decay. \n\nThree isotopes have been mentioned in the question - \({ }^{14} \mathrm{C}\) (carbon-14), \({ }^{15} \mathrm{O}\) (oxygen-15) and \({ }^{3} \mathrm{H}\) (hydrogen-3 or tritium). Of these, carbon-14 has a half-life of 5730 years, oxygen-15 has a half-life of 124 seconds, and tritium has a half-life of 12.5 years.
02

Phase 2 - Selecting the Correct Isotope for Dating

The aim of the study is to confirm the age of a wine bottle sealed 6 years ago. So, the isotope selected for radioactive dating should ideally have a half-life closer to 6 years. That's because if an isotope's half-life is significantly longer than the time period being studied, most of the isotope won't have decayed over that period, which means it wouldn't provide a precise age.
03

Phase 3 - Confirming the Age of the Wine Bottle

Comparing the half-lives of the three isotopes, it can be seen that tritium (\({ }^{3} \mathrm{H}\)) with a half-life of 12.5 years is the closest to the 6-year period. Although it's not an exact match, tritium would still be a better choice than carbon-14 or oxygen-15, as long as the activities of the isotopes were known when the bottle was sealed. So, the tritium isotope should be used for the radioactive dating study to confirm the age of the wine bottle.

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