Question

The constituents of wine contain, among others, carbon, hydrogen, and oxygen atoms. A bottle of wine was sealed about 6 years ago. To confirm its age, which of the isotopes would you choose in a radioactive dating study? The half-lives of the isotopes are: \({ }^{14} \mathrm{C}: 5715\) years; \({ }^{15} \mathrm{O}: 124 \mathrm{~s} ;{ }^{3} \mathrm{H}: 12.5\) years. Assume that the activities of the isotopes were known at the time the bottle was sealed.

Short answer

Use \\(^{3} \mathrm{H}\\) for dating the wine, as its half-life is suitable for a 6-year-old sample.

Step-by-step solution

Identify the Elements Involved

The problem states that wine contains carbon, hydrogen, and oxygen. Therefore, the isotopes we need to consider for dating are \({ }^{14}\mathrm{C}\), \({ }^{15}\mathrm{O}\), and \(^{3}\mathrm{H}\).

Evaluate the Half-Lives

Review the half-lives: \({ }^{14} \mathrm{C}: 5715\) years, \({ }^{15} \mathrm{O}: 124\) seconds, and \({ }^{3} \mathrm{H}: 12.5\) years.

Consider the Age of the Sample

The wine bottle is 6 years old. This is less than the half-life of \(^{14}\mathrm{C}\) and \(^{3}\mathrm{H}\), but is much longer than the half-life of \(^{15}\mathrm{O}\). \({ }^{15}\mathrm{O}\) has already decayed completely due to its short half-life.

Choose a Suitable Isotope for Dating

The appropriate isotope for dating should have a half-life relatively close to the age of the sample. \({ }^{14} \mathrm{C}\) has a much larger half-life compared to the age, so using it would not allow for precise dating in such a short period. \({ }^{3} \mathrm{H}\), with a half-life of 12.5 years, is suitable for dating a 6-year-old sample because it is comparable to the sample's age.

Key concepts

Isotopes

In the world of chemistry and physics, isotopes are variations of elements that contain the same number of protons but different numbers of neutrons. This means they have the same atomic number but different mass numbers.
Each isotope of an element will have a unique set of chemical properties, which can be used to measure the age or to trace certain chemical processes.
In our radioactive dating example, isotopes of Carbon-14, Tritium, and Oxygen-15 are used. They are important for their ability to decay at known rates, a property which allows them to serve as natural clocks.

• Stable vs. Unstable Isotopes: Stable isotopes do not change over time, while unstable isotopes decay, releasing particles or radiation.
• Radioactive Decay: This is a random process but happens at a predictable rate for a large collection of atoms. It's the decay of unstable isotopes that make them useful for dating.

Half-life

Half-life is a fundamental concept in radioactive dating. It refers to the time it takes for half of a given sample of a radioactive isotope to decay into another element.
It's crucial for determining the age of materials because it is both constant and unique for each isotope. By measuring the remaining amounts of an isotope, scientists can calculate how many half-lives have passed and estimate the sample's age.

• Exponential Decay: Radioactive decay is an exponential process. If you start with a 100g sample of a radioactive isotope with a half-life of 10 years, after 10 years, only 50g of it will remain.
• Importance in Dating: A suitable half-life is vital for effective dating. It should be on a similar scale to the age of the sample to provide meaningful dating information.

Carbon-14

Carbon-14 is one of the most commonly used isotopes in radioactive dating. Known for its ability to date substances containing organic materials, it has a half-life of about 5715 years.
This means it is particularly useful for dating archaeological finds, cave paintings, or historical artifacts, where age plays a critical role.

• Production: Carbon-14 is created in the Earth's atmosphere through the interaction of cosmic rays with nitrogen.
• Usage Limitation: Because of its half-life, it is not practical for dating materials that are only a few years or decades old, like our wine bottle from the exercise.

Tritium

Tritium, also known as ^{3}H, is a radioactive isotope of hydrogen. It has a half-life of 12.5 years, making it a good candidate for dating materials on the scale of decades, rather than centuries or millennia.
This property is what makes tritium suitable for the 6-year-old wine from our exercise.

• Natural and Artificial Sources: Tritium occurs both naturally and as a product from nuclear reactors or weapons testing.
• Applications: Besides dating, tritium is used in luminous devices like watch dials and exit signs.

Oxygen-15

Oxygen-15 is an isotope with a notably short half-life of just 124 seconds. Due to its rapid decay, it is not feasible for dating anything beyond a minute or so.
This makes oxygen-15 unsuitable for dating purposes like in our exercise, where the sample is several years old.

• Medical Use: Oxygen-15 is often used in medical imaging procedures such as Positron Emission Tomography (PET) scans due to its rapid decay, which provides detailed images of body processes in real-time.
• Limitations in Dating: As it decays too quickly, oxygen-15 is not used in radioactive dating.