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# The half-life of an isotope is the amount of time required f

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Retired Moderator
Joined: 07 Jun 2014
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The half-life of an isotope is the amount of time required f [#permalink]  27 Jul 2018, 07:05
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Question Stats:

70% (01:37) correct 30% (02:37) wrong based on 20 sessions
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
[Reveal] Spoiler: OA

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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3037 [0], given: 394

Re: The half-life of an isotope is the amount of time required f [#permalink]  12 Aug 2018, 05:06
Expert's post
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.
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Re: The half-life of an isotope is the amount of time required f   [#permalink] 12 Aug 2018, 05:06
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