The half-life for radioactive decay of 14C is 5730 years. An archaeological artifact containing wood had only 80% of the 14C found in a living tree. Estimate the age of the sample.
Question
The half-life for radioactive decay of 14C is 5730 years. An archaeological artifact containing wood had only 80% of the 14C found in a living tree. Estimate the age of the sample.
Solution
To estimate the age of the sample, we can use the formula for radioactive decay, which is:
N = N0 * (1/2)^(t/T)
where: N is the final quantity of the substance N0 is the initial quantity of the substance t is the time that has passed T is the half-life of the substance
In this case, we know that N/N0 is 80%, or 0.8, and T is 5730 years. We want to solve for t.
0.8 = (1/2)^(t/5730)
To solve for t, we can take the natural logarithm of both sides:
ln(0.8) = (t/5730) * ln(1/2)
Then, solve for t:
t = 5730 * ln(0.8) / ln(1/2)
This gives us t ≈ 1600 years. So, the archaeological artifact is approximately 1600 years old.
Similar Questions
The half life for the radioactive decay of carbon-14 to nitrogen-14 is ×5.73103 years.Suppose nuclear chemical analysis shows that there is 0.414mmol of nitrogen-14 for every 1.000mmol of carbon-14 in a certain sample of rock. Calculate the age of the rock.Round your answer to 2 significant digits.
The half-life of carbon-14, 14C, is approximately 5,730 years. A bone fragment is estimated to have originally contained 4 milligrams of 14C.Write the exponential decay equation where A is the amount (in mg) of carbon-14 remaining in the bone fragment after t years.
The half-life of the radioactive carbon isotope 14C is 5730 yr. A wooden artefact contains only 12.5% of the original content of this isotope. How old is the artefact? 17,190 yr 22,920 yr 57,300 yr 28,650 yr 45,840 yr
Carbon-14 is a radioactive nucleus with a half-life of 5760 years. In livingmatter the amount of carbon-14 decays at a rate of 15.3 decay events perminute per gram of carbon. A fossil is analysed and found to have a carbon-14 decay rate of 7.70 decay events per minute per gram of carbon. How oldis the fossil?
Select the correct answer.The amount of a radioactive substance remaining as it decays over time is 𝐴=𝐴0(0.5)𝑡ℎ , where A represents the final amount, 𝐴0 represents the original amount, t represents the number of years, and h represents the half-life of the substance.Carbon-14 is a radioactive isotope that has a half-life of 5,730 years. Approximately how many years will it take for carbon-14 to decay to 10 percent of its original amount? A. 16,396 years B. 19,035 years C. 28,650 years D. 8,267 years
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.