4) After three half-lives of an isotope, 1 billion (one-eighth) of the original isotope's atoms still remain in a certain amount of this element. How many atoms of the daughter product would you expect to be present?

7 * 10^9 atoms

Explanation:

We must first find the number of atoms originally present. We can do this by considering the information given in the question that one-eight of the original isotope is left and that is about one billion atoms of the original material left. Let the number of atoms originally present be x.

So;

1/8x = 1 * 10^9

x = 8/1 * 1 * 10^9

x = 8 * 10^9 atoms of radioactive material.

Number of atoms of daughter nucleus present=

x- 1/8x = 7/8x

but x = 8 * 10^9 atoms of radioactive material

Therefore;

7/8 * 8 * 10^9 atoms = 7 * 10^9 atoms