If an isotope has a half-life of 50 million years,and 1/8 of the sample remaining consists of that isotope,what is the age of the rock from which it was taken?
A) 400 million years
B) 300 million years
C) 150 million years
D) 800 million years
E) none of these

Question

Quizplus · Accepted Answer

If only 1/8 of the sample remaining consists of the isotope, then 7/8 of the sample has decayed.

We can use the formula:

(1/2)^(n) = (1/8)

Where n is the number of half-lives that have occurred.

Simplifying, we get:

(1/2)^(n) = (1/2)^3

n = 3

So, three half-lives have occurred. Since the half-life is 50 million years, the age of the rock is:

3 x 50 million years = 150 million years.

If an Isotope Has a Half-Life of 50 Million Years,and