You have before you two glasses of Amontillado wine - one made last year and one

Question

You have before you two glasses of Amontillado wine - one made last year and one made many years ago. You have claimed to be an expert wine connoisseur (now that you are 21 years old, of course) and able to "taste the age" of the wine. If you can determine which one is older, and its age, then you receive an entire cask of this wine! Unfortunately, you have a cold and cannot taste any difference between the two. Luckily, you have your handy-dandy pocket instrument that is capable of detecting (e.g., counting) tritium decay (tritium is a naturally-occurring, radioactive isotope of hydrogen). Tritium undergoes beta-decay with a half-life of 12.26 years. The glass on the left has sixty-four times fewer tritium counts than the glass on the right.

Explanation / Answer

Suppose intially, the sample on the left contained 64x number of tritium atoms initially (just like the new sample on the right). Now it contains x number of tritium atoms. The formula of radioactive decay is

N(t) = N(o) (1/2) ^ t/t1/2

N(t) = x, N(o) = 64x, t1/2 = 12.26 yrs, t = ?

N(t) = N(o) (1/2) ^ t/t1/2

x = 64x (1/2) ^ t/12.26 yrs

or, 1/64 = (1/2) ^ t/12.26 yrs

or, (1/2) ^6 = (1/2) ^ t/12.26 yrs

or, t/12.26 = 6

or, t = 73.56 yrs

The old wine is 73.56 yrs old

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.