A radioactive element has a half-life of 1000 years. If a sample of this element begins with a mass of 20 grams how long would you have to wait for the mass to decrease to 5 grams?

Since the element has a half-life of 1000 years, it will take two half-lives for the mass to decrease to 5 grams from 20 grams. Two half-lives equal 2000 years, so you would have to wait 2000 years for the mass to decrease to 5 grams.