To calculate the time it will take for the number of undecayed atoms in a sample to fall to one-eighth of their original number, we can use the concept of half-life.Given that the half-life of the radioactive substance is 13 years, we know that after every 13 years, the number of undecayed atoms will be reduced by half.Let's assume the original number of undecayed atoms is represented by N.After the first half-life (13 years), the number of undecayed atoms will be N/2.
After the second half-life (another 13 years), the number of undecayed atoms will be (N/2)/2 = N/4.
After the third half-life (another 13 years), the number of undecayed atoms will be (N/4)/2 = N/8.Since we're looking for the time it takes for the number of undecayed atoms to fall to one-eighth of their original number, we can see that it takes 3 half-lives, each lasting 13 years.Therefore, it will take 3 * 13 = 39 years for the number of undecayed atoms in the sample to fall to one-eighth of their original number.