500
The half-life of one isotope of radium is about 1600 years. In a given sample of this isotope, 15 over 16 of the radium atoms will decay in a time most nearly equal to?
6,400 years
During each half-life, an average of 1 over 2 of the nuclei present will decay. So after one half-life only about 1 over 2 of the radium nuclei remain. After two half-lives the sample contains 1 over 2 of 1 over 2 , or about 1 over 4 of the original number of radium nuclei. In general, the number of nuclei remaining after n half-lives have elapsed is(1 over 2)^n.Having 15 over 16 of the radium nuclei decay means having 1 over 16 of them remain, which is (1 over 2)^4. So the answer is four half-lives, which is 6400 years.