1.The remains of an old campfire are unearthed and it is found that there is only 80% as much radioactive carbon-14 in the charcoal samples from the campfire as there is in modern living trees. If the half-life of carbon- 14 is 5730 years, how long ago did the campfire burn?
Po = Poe^kt
1/2 = e^5730k
Ln(1/2) = Lne^5730k
Ln(1/2) = 5730k
K = ln(1/2)/5730
Poe^ln(1/2)/5730 *t
.80P0 = Poe^ln(1/2)/5730 *t
.8 = e^ln(1/5)/5730 t
ln(.8) = ln(.5)/5730t lne
ln(.8) = ln(.5)/ 5730 t
t = 5730ln(.8)/ln(.5)
t=1844.65 years
found in an Egyptian pyramid contains 75% of its original carbon_14 which has about 5730 years as half-life.
To determine how long ago the campfire burned, we can use the concept of radioactive decay and the half-life of carbon-14. Here's how you can calculate it:
1. Start by understanding what half-life means. The half-life of carbon-14 is the time it takes for half of a given amount of carbon-14 to decay. In this case, the half-life of carbon-14 is 5730 years.
2. Since the campfire charcoal samples have only 80% as much radioactive carbon-14 as modern living trees, we can calculate the ratio of the remaining carbon-14 in the campfire samples to the original amount found in living trees. This ratio is 0.80.
3. Now, we need to determine the number of half-lives that have passed. To do this, use the following formula:
Number of half-lives = log(base 0.50) of (ratio)
In this case, the ratio is 0.80, so the formula becomes:
Number of half-lives = log(base 0.50) of (0.80)
Using a calculator, the result is approximately 0.322
4. Now, we can find the time that has passed since the campfire burned by multiplying the number of half-lives by the half-life of carbon-14:
Time = number of half-lives x half-life of carbon-14
Time = 0.322 x 5730 years
The result is approximately 1,847 years.
Therefore, the campfire burned approximately 1,847 years ago.