An artifact was found and tested for its carbon-14 content. If 84% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? Use that carbon-14 has a half-life of 5,730 years.
0.84 = (0.50)^(t/5730)
t/5730 = log0.85/log0.50 = 0.23447
t = 1343 years
(Round it to 1300 years)
The half-life of 234U, uranium-234, is 2.2.52 x 10 5th power years. If 97.4% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed?
To determine the probable age of the artifact, we can use the concept of carbon-14 dating. Carbon-14 is an isotope of carbon that is naturally present in the atmosphere and is absorbed by living organisms. When an organism dies, it no longer absorbs new carbon-14, and the existing carbon-14 begins to decay.
The half-life of carbon-14 is 5,730 years, which means that every 5,730 years, half of the original carbon-14 will decay. In this case, we are told that 84% of the original carbon-14 is still present. Therefore, 16% (100% - 84%) of the carbon-14 has decayed.
Since the half-life is 5,730 years, we can calculate the number of half-lives that have occurred by dividing the percent decayed (16%) by 50% (half of 100%). This gives us 0.32 half-lives (16% / 50%).
Next, we can determine the number of years that have passed based on the number of half-lives. Multiply the number of half-lives (0.32) by the half-life of carbon-14 (5,730 years). This gives us approximately 1,833.6 years (0.32 * 5,730).
Finally, to get the probable age of the artifact, we can round the result to the nearest 100 years. In this case, the probable age of the artifact is 1,800 years.
Therefore, based on the given information, the probable age of the artifact is approximately 1,800 years.