The half-life of a radioactive isotope is 10,000 years. This isotope and its breakdown product do not normally occur together when molten rock cools and becomes solid. If you have a volcanic rock sample containing 0.25 grams of the radioactive isotope and 0.75 grams of its breakdown product, when did this rock likely solidify?
A) 2,500 years ago
B) 50,000 years ago
C) 10,000 years ago
D) 20,000 years ago

Question

Quizplus · Accepted Answer

The rock likely solidified 20,000 years ago. Initially, there would have been 1 gram of the radioactive isotope and no breakdown product. After the first half-life (10,000 years), half of the isotope would have decayed, leaving 0.5 grams of the isotope and 0.5 grams of the breakdown product. After the second half-life (another 10,000 years, totaling 20,000 years), half of the remaining isotope would have decayed again, leaving 0.25 grams of the isotope and increasing the breakdown product to 0.75 grams.

The Half-Life of a Radioactive Isotope Is 10,000 Years