A rock contains 18 mg of the radioactive isotope carbon-14. The half-life of carbon-14 is 5,600 years. How many half-lives and years will it take before the carbon-14 decays to less than 4 mg?

Question

A.  1 half-lives; 5,600 years
B.  2 half-lives; 11,200 years
C.  3 half-lives; 16,800 years
D.  4 half-lives; 22,400 years
E.  9 half-lives; 50,400 years

Clarify Question
What is the key concept addressed by the question?
What type of thinking is required?

  Gather Content
What do you already know about half-lives of radioactive isotopes? What other information is related to the question?

Choose Answer
Given what you now know, what information is most likely to produce the correct answer?
 
Reflect on Process
Did your problem-solving process lead you to the correct answer? If not, where did the process break down or lead you astray? How can you revise your approach to produce a more desirable result?
 

Answer 1

C.  3 half-lives; 16,800 years

Clarify Question
What is the key concept addressed by the question?
        · The question stem is asking you to calculate how many half-lives would occur in order to have less than 4 mg left of the original 18 mg of radioactive carbon-14.
What type of thinking is required?
        · You are being asked to take what you already know and use, or apply, it to the half-life of the radioactive isotope, carbon-14.

  Gather Content
What do you already know about half-lives of radioactive isotopes? What other information is related to the question?
        · Isotopes decay at a known rate, called their half-life. During each half-life, one-half of the original amount of parent isotope has transformed into a daughter isotope. Therefore, if a sample of material had 10 g of radioactive isotope and a half-life of 3 hours, then after three hours, or one half-life, the sample would have 5g of radioactive isotope and 5 g of the daughter isotope. After six hours, or two half-lives, the sample would have 2.5 g of radioactive isotopes and 7.5 g of the daughter isotope.
 
Choose Answer
Given what you now know, what information is most likely to produce the correct answer?
        · The half-life of carbon-14 is 5,600 years. Therefore, after 5,600 years, the 18 mg sample of carbon-14 would have 9 mg of carbon-14 left. How many mg would be left after 11,200 years? What about after three half-lives? What about after four or even nine half-lives?
 
Reflect on Process
Did your problem-solving process lead you to the correct answer? If not, where did the process break down or lead you astray? How can you revise your approach to produce a more desirable result?
       · Answering this question correctly depended on your ability to use the concept of half-life in a new situation¼ If you got an incorrect answer, did you remember that half-life is the time it takes for one half of a sample of radioactive isotope to decay into the daughter isotope, or that the amount of time affects how many half-lives have occurred? Did you have trouble extending half-life to determine the correct answer?