an artifact has a starting mass of C-14 of 200 g and a remaining mass of 0.78125 g. how old if the artifact?
[4.58^4 years]
.78125=200e^(ln2*t/thalf)
take the ln of both sides.
ln(.78125)=ln200+ln2*t/thalf
HALF-LIFE 3 CONFIRMED
To determine the age of the artifact, we need to use the concept of radioactive decay and the half-life of C-14.
Before explaining how to calculate the age of the artifact, it's essential to understand the basic principles involved:
1. C-14 is an isotope of carbon that undergoes radioactive decay over time.
2. The half-life of C-14 is approximately 5730 years. This means that after 5730 years, half of the initial amount of C-14 in a sample will have decayed.
3. By measuring the remaining fraction of C-14 in an artifact, we can estimate how long it has been since the organism that the artifact is made of died.
Now, let's calculate the age of the artifact:
1. We know that the initial mass of C-14 in the artifact was 200 g, and the remaining mass is 0.78125 g.
2. To find the fraction of remaining C-14, we divide the remaining mass by the initial mass:
Fraction of remaining C-14 = Remaining mass / Initial mass
= 0.78125 g / 200 g
= 0.00390625
3. Now, we need to determine how many half-lives have occurred to reach this fraction of remaining C-14. This can be done using the formula:
Number of half-lives = log(base 0.5) of (Fraction of remaining C-14)
By applying this formula, we can find that the number of half-lives is approximately 4.58.
4. Since each half-life of C-14 is approximately 5730 years, we can calculate the age of the artifact:
Age of artifact = Number of half-lives * Half-life duration
= 4.58 * 5730 years
≈ 26,271.9 years or approximately 26,272 years.
Therefore, based on the given information, the age of the artifact is estimated to be approximately 26,272 years.