Question

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

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

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.

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.

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.

Key concepts

Isotopes

Isotopes are fascinating variations of the same chemical element, differing in the number of neutrons in their atomic nucleus. This means while they have the same number of protons or "atomic number," their "mass number," which is the total of protons and neutrons, can vary. Despite these differences, isotopes of an element generally share similar chemical properties. However, when it comes to radioisotopes, things get a bit interesting.
These radioisotopes are unstable isotopes that decay over time and release radiation in the process. Radioactive dating leverages this property to determine the age of substances. This decay happens at remarkable rates that are characteristic of each isotope. Capturing this dynamic property is essential in various scientific studies, from archaeology to geology. Think of isotopes as same-child-different-dress siblings in the atomic world!
Understanding isotopes forms the backbone of radioactive dating, as it elucidates why different isotopes are chosen for dating substances of varying ages.

Half-Life

The half-life of an isotope is a vital concept in radioactive dating. It is defined as the amount of time it takes for half of a sample of a radioactive isotope to decay. This decay process is exponential, meaning that with every passing half-life, half of the remaining isotope continues to decay. This predictable pattern forms the foundation of using half-life in dating methods.
To visualize, if you start with 100 atoms of a radioactive isotope, after one half-life, only 50 atoms would remain unchanged; the rest transforms into another element or a different isotope. After another half-life, only 25 atoms of the original isotope would be left, and so on. The intriguing part is that each isotope has its own unique half-life - some just a few moments long, while others span thousands of years.
In the case of our wine bottle exercise, identifying the correct isotope for dating greatly relies on selecting an isotope with a half-life close to the age being studied. A short half-life would mean the isotope decays too quickly, while an overly long half-life would see little change over the studied period.

Tritium

Tritium, also known as hydrogen-3, is an isotope of hydrogen with two neutrons and one proton in its nucleus. This addition of neutrons compared to the more common hydrogen isotopes makes tritium slightly heavier. Tritium is naturally radioactive and decays by releasing beta particles, which are essentially electrons or positrons emitted from the atomic nucleus.
This decay property is perfectly manageable due to tritium's half-life of 12.5 years. Compared to thousands of years or mere seconds for other isotopes, this time frame can conveniently match mid-length periods, like the 6-year-old wine bottle we are analyzing.
Tritium is widely used in scientific studies, especially in research involving water, since it mimics the behavior of hydrogen in water. In the context of the exercise, tritium is chosen for its half-life proximity to the six-year period, making it particularly handy for age confirmation. As with the wine bottle, understanding tritium's decay allows scientists to assess periods that aren’t too short or too long - precisely the kind of middle-ground many researchers seek in radioactive dating.