# How much material will be left if a radioactive isotope has a half life of 1.3 billion years in 3.9 billion years?

Jul 21, 2014

You will have 12.5 % of the parent material after 1.3 billion years.

This problem is like the one at

http://socratic.org/questions/if-half-life-is-2-hours-approximately-what-percent-is-left-after-11-8-how-would-

Method 1

In your problem, the number of half-lives is

$n$ = 3.9 billion years × $\left(1 \text{half-life")/(1.3"billion years}\right)$ = 3.0 half-lives

The amount remaining after 3 half-lives is

100 % × 1/2 × 1/2 ×1/2 = (100"%")/8 = 12.5 %

Method 2

A=A_0/2^n = (100 %)/2^3.0 = 12.5 %