Question
If 70% of a radioactive element remains radioactive after 400 million years , then what percent remains radioactive after 600 million years? What is the half-life of this element
Answers
Steve
If the half-life is k years, then after t years,
(1/2)^(t/k)
remains. Thus, to find k, solve
(1/2)^(400/k) = 0.7
600 = 3/2 * 400, or 1.5 half-lives. So, the amount remaining after 600 mega years is
(1/2)^(3/2 * 400/k)
= (1/2)^(400/k)^(3/2)
= 0.7^(3/2)
= ?
(1/2)^(t/k)
remains. Thus, to find k, solve
(1/2)^(400/k) = 0.7
600 = 3/2 * 400, or 1.5 half-lives. So, the amount remaining after 600 mega years is
(1/2)^(3/2 * 400/k)
= (1/2)^(400/k)^(3/2)
= 0.7^(3/2)
= ?