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The half-life of an isotope is the amount of time required f
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27 Jul 2018, 07:05
27 Jul 2018, 07:05
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The half-life of an isotope is the amount of time required for 50% of a sample of the isotope to undergo radioactive decay. The half-life of the carbon-14 isotope is 5,730 years. How many years must pass until a sample that starts out with 16,000 carbon-14 isotopes decays into a sample with only 500 carbon-14 isotopes?
(A) 180 years
(B) 1,146 years
(C) 5,730 years
(D) 28,650 years
(E) 183,360 years
(A) 180 years
(B) 1,146 years
(C) 5,730 years
(D) 28,650 years
(E) 183,360 years
Re: The half-life of an isotope is the amount of time required f
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12 Aug 2018, 05:06
12 Aug 2018, 05:06
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Expert Reply
Explanation
After each half-life, the sample is left with half of the isotopes it started with in the previous period. After one half-life, the sample goes from 16,000 isotopes to 8,000. After two half-lives, it goes from 8,000 to 4,000.
Continue this pattern to determine the total number of half-lives that have passed: 4,000 becomes 2,000 after 3 half-lives, 2,000 becomes 1,000 after 4 half-lives, 1,000 becomes 500 after 5 half-lives. The sample will have 500 isotopes after 5 half-lives. Thus, multiply 5 times the half-life, or 5 × 5,730 = 28,650 years.
Note that the answer choices are very spread apart. After determining that 5 half-lives have passed, estimate: \(5 \times 5,000 = 25,000\) years; answer (D) is the only possible answer.
After each half-life, the sample is left with half of the isotopes it started with in the previous period. After one half-life, the sample goes from 16,000 isotopes to 8,000. After two half-lives, it goes from 8,000 to 4,000.
Continue this pattern to determine the total number of half-lives that have passed: 4,000 becomes 2,000 after 3 half-lives, 2,000 becomes 1,000 after 4 half-lives, 1,000 becomes 500 after 5 half-lives. The sample will have 500 isotopes after 5 half-lives. Thus, multiply 5 times the half-life, or 5 × 5,730 = 28,650 years.
Note that the answer choices are very spread apart. After determining that 5 half-lives have passed, estimate: \(5 \times 5,000 = 25,000\) years; answer (D) is the only possible answer.
Re: The half-life of an isotope is the amount of time required f
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08 Jul 2021, 01:55
08 Jul 2021, 01:55
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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