Question

6. Radiometric Dating. You are analyzing rocks that contain small amounts of potassium-40 and argon-40. The half-life of potassium-40 is 1.25 billion years. Assume for simplicity that potassium-40 decays only into argon-40.

       a. You find a rock that contains equal amounts of potassium-40 and argon-40. How old is it? Explain.

       b. You find a rock that contains three times as much argon-40 as potassium-40. How old is it? Explain.

       c. Assume that any radioactive element decays to undetectable levels after 20 half-lives. Use this fact and data about radioactive elements present in Earth’s crust to estimate a minimum age for the Earth. (A minimum age is useful for testing more detailed calculations. See “Listing of Persistent Nuclides by Half-life” in the Formation of the Solar System Lecture. Assume “Found in Nature” in the table means “Found in Earth’s crust.”)

       d. Explain why you can’t use carbon-14 to date the age of meteorites.

Answer 1

(a) Since potassium decays only into argon, and the sample has equal amount of potassium and argon so it is clear that half of the potassium is decayed and forms argon. Since the half-life of potassium-40 is 1.25 billion years, the rock has to be 1.25 billion years old.

(b) Three times as much argon means that potassium is 1/4 and argon is 3/4.

Potassium will be 1/4 only after two half lives. Since the half-life of potassium-40 is 1.25 billion years, the rock has to be 2.5 billion years old after two half lives.

(c) Most of the Earth crust has Carbon 14 which has a half life of 6000 years. So after 20 half life, it will be 20*5000 = 12,000 years.

(d) Carbon 14 is has a very short half life so it cannot date the age of metorites which are million of years old.

answered by: anonymous