Question

A radioactive substance is made up of 2,000 atoms, and after decaying for 20 years only 125 atoms of the parent isotope remain. What is the half-life of the substance in years?

a) 5 years
b) 10 years
c) 15 years
d) 20 years

Answer 1

To determine the half-life, we see that in 20 years, the radioactive substance decays from 2,000 to 125 atoms, which corresponds to 4 half-lives. Therefore, the half-life is 20 years divided by 4, which is 5 years.

Step-by-step explanation:

The question is asking for the half-life of a radioactive substance. To find the half-life, you can use the fact that after one half-life, there is half of the original amount of the substance remaining. In the given example, 2,000 atoms decay to 125 atoms after 20 years. This process includes more than one half-life, so let's calculate how many half-lives are there. After the first half-life, you would have 1,000 atoms remaining (half of 2,000), after the second half-life, there would be 500 atoms left, after the third, 250 atoms, and after the fourth half-life, there would be 125 atoms. Since it takes four half-lives to get from 2,000 to 125 atoms and the total time is 20 years, we can divide 20 years by 4 to find the half-life.