The half-life of a certain radioactive element is 800 years. How old is an object if only 12.5% of the radioactive atoms in it remain?

Answer 1

An easy way to approach these types of problems (in my opinion) is to use the following equation:

Fraction Remaining = 0.5ⁿ

n = # of half lives that have elapsed

In the current problem, we are given the fraction remaining as 0.125 (12.5%)

We are also given the half life of 800 years, and we are asked to find the age of the object. To do this, we will find how many half lives have elapsed and then simply multiply that by the number of years in 1 half life.

0.125 = 0.5ⁿ

log 0.125 = n log 0.5

-0.903 = -.301 n

n = 3 half lives have elapsed

3 half lives x 800 years/half life = 2400 years = age of the object