A bottle of red wine is thought to have been sealed about `5 years` ago. The wine containa a number of different kinds of atoms, incluing carbon, oxygen,and hydrogen. Each of these has a radioactive isotope. The radiaoctive isotope of carbon is the familiar `._6^(14)C` with a half-life of `5730 years`. The radioactive isotope of oxygen is. `._(8)^(15)O` and has a half-life of `122.2 s`. The radioactive isotope of hydrogen `._1^(3)H` and is called tritium, its half-life is `12.33 years`. The activity of each of these isotopes is known at the time the bottle was sealed. However, only one of the isotopes is useful for determining the age of the wine accurately. Which is it?

Explanation

In a dating method that measures the activity of radioactive isotope, the age of the sample is realted to the change in the activity during the time period in question. Here, the expected age is about `5 years`. This period is only a small fraction of the `5730 - year` half -life `._6^(14)C` . As a result, relatively few of the `._6^(14)C` nuceli would decay during the wine's life, and the measured activity would change little from its initial value. To obtain an accurate age from such a small change would reqquire prohibiitively precise measurements. Nor is the `._8^(15)O` is isotpe very useful. The difficulty is its relatively short half -life of `122.2 s`. During a `5 -year` period, so many half -lives of `122.2 s` small level. It would not be even possible to measure it. The expected. age of `5 years` that a measurable change in activity will have completely vanished for all practical purposes.