A rock formed with 1,000 atoms of a radioactive parent element, but only contains 125 radioactive parent atoms today. If the half life is 1,000,000 years, how old is the rock?

The rock is three million years.

Explanation:

First, we need to understand what half-life means. It is a period of time in which the radioactivity of the source decreases to the half of its original value (the number of radioactive atoms decreases to half). We started off with 1000 atoms, which means that after one period of half time, the number will decrease to 500. So after million years we are left with 500 atoms. After another million years the number will decrease to 250 atoms. After the next half time period, the number will decrease to 125.

So:

1 half time: from 1000 to 500

2 half time: from 500 to 250

3 half time: from 250 to 125

So the number of atoms decreased from 1000 to 125 after 3 half time periods, which is after 3 million years.