Element A decays into element B with a half-life of 700 million years. An astronomer finds a rock that she knows was formed originally without any B present. But the rock now contains both A and B, with the A+B portion of the rock being 1/8 A and 7/8 B. How old is the rock?
A) 350 million years
B) 700 million years
C) 1.4 billion years
D) 2.1 billion years

Question

Quizplus · Accepted Answer

The rock is 2.1 billion years old. Initially, the rock was all A with no B. After each 700 million years (the half-life of A), the amount of A halves. The ratio of A to B is 1/8 to 7/8, indicating that three half-lives have passed (since $1/2^3 = 1/8$), totaling 2.1 billion years (700 million years x 3).

Element a Decays into Element B with a Half-Life of 700