Question

A Scotch-drinking physicist suspects the 50-year-old Scotch she purchased was misrepresented. Reasoning that water must contain tritium because this isotope is produced in the atmosphere by cosmic rays, she uses the 3H concentration in the Scotch to determine when it was bottled. She finds that the 3H concentration in the Scotch was 64% that of the 3H concentration in the water on the Isle of Islay, where the Scotch was bottled. Approximately how old is this “50-year-old” Scotch? (The half-life of tritium is 12.3 years.)

Answer 1

The 50-year-old Scotch is actually approximately 19 years old.

Step-by-step explanation:

In order to determine the approximate age of the '50-year-old' Scotch, we can use the concept of tritium dating. Tritium is a radioactive isotope of hydrogen with a half-life of 12.3 years. By comparing the concentration of tritium in the Scotch to the concentration in the water on the Isle of Islay, where the Scotch was bottled, we can estimate its age.

The question states that the tritium concentration in the Scotch is 64% that of the tritium concentration in the water on the Isle of Islay. This means that the tritium in the Scotch has undergone multiple half-lives.

Using the formula for radioactive decay, we can calculate the number of half-lives that have passed:

1. Let x be the number of half-lives that have passed.
2. Since each half-life reduces the concentration by half, we can set up the equation: (1/2)^x = 0.64.
3. Taking the logarithm of both sides, we find: x = log(0.64) / log(1/2).
4. Using a calculator, we find x ≈ 1.557.

Therefore, approximately 1.557 half-lives have passed. Considering that the half-life of tritium is 12.3 years, we can multiply the number of half-lives by the half-life to find the approximate age of the Scotch:

Age ≈ 1.557 * 12.3 ≈ 19.121 years.

Thus, the '50-year-old' Scotch is actually approximately 19 years old.