A certain element has a half-life of 1,000 years. How much of a sample of this element remains after 2,000 years?

A quarter of the sample.

Explanation:

Let the quantity at the beginning be T. If the element has a half-life of 1,000 years, it means that after 1000 years, T/2 (which represents half the initial quantity available) would have decayed, remaining T/2.

After another 1000 years (making 2000 years), T/4 (which represents have of the quantity left after the first 1000 years) would have decayed, remaining T/4.

This means that only a quarter of T would be left after 2000 years.