Final answer:
Carbon-14 has a half-life of 5,730 years. It would take 11,460 years for 25% of the original amount of carbon-14 in the sample to decay. After five half-lives, 7.5 grams of carbon-14 would remain.
Step-by-step explanation:
(a) To determine how many years it would take for % of the original amount of carbon-14 in the sample to decay, we can use the concept of half-life. The half-life of carbon-14 is 5,730 years. After each half-life, the amount of carbon-14 remaining is halved. So, if we want to determine how many years it would take for 25% of the original amount to decay, we can calculate the number of half-lives required.
Since 50% is remaining after the first half-life, then 25% should remain after the second half-life. This means it would take two half-lives or 2 x 5,730 = 11,460 years for 25% of the original amount to decay. Therefore, the answer is B) 11,460 years.
(b) After five half-lives, the amount of carbon-14 remaining can be calculated by repeatedly halving the sample size. The equation for calculating the remaining amount after n half-lives is given by:
Remaining amount = Initial amount x (1/2)^n.
For five half-lives, we plug in n = 5 and the initial amount of 120 grams to calculate the remaining amount:
Remaining amount = 120 grams x (1/2)^5 = 7.5 grams.
Therefore, the answer is B) 7.5 grams.