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The half-life of an isotope is the amount of time required for 50% of
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23 Mar 2021, 09:45
23 Mar 2021, 09:45
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50% (01:05) correct
50% (01:44) wrong based on 6 sessions
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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 under-go 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?
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\(28,650\)
Re: The half-life of an isotope is the amount of time required for 50% of
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24 Mar 2021, 10:50
24 Mar 2021, 10:50
solution plz
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
The half-life of an isotope is the amount of time required for 50% of
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24 Mar 2021, 22:18
24 Mar 2021, 22:18
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Explanation:
It takes carbon-14 isotope sample \(5,730\) years to decay to half of the amount
Let us count the decays from \(16,000\) to \(500\)
\(\frac{16,000}{2} = 8,000\)
\(\frac{8,000}{2} = 4,000\)
\(\frac{4,000}{2} = 2,000\)
\(\frac{2,000}{2} = 1,000\)
\(\frac{1,000}{2} = 500\)
Since, we have \(5\) decays and each decay will take \(5,730\) years. Therefore, \((5)(5,730) = 28,650\) years
It takes carbon-14 isotope sample \(5,730\) years to decay to half of the amount
Let us count the decays from \(16,000\) to \(500\)
\(\frac{16,000}{2} = 8,000\)
\(\frac{8,000}{2} = 4,000\)
\(\frac{4,000}{2} = 2,000\)
\(\frac{2,000}{2} = 1,000\)
\(\frac{1,000}{2} = 500\)
Since, we have \(5\) decays and each decay will take \(5,730\) years. Therefore, \((5)(5,730) = 28,650\) years
