Carbon-14 has a half-life of 5730 . In a plant fossil, you find that the has decayed to 1/32.0 of the original amount. How long ago was this plant alive?
k = 0.693/t1/2
Solve for k.
ln(No/N) = kt
You can make No any convenient number. I would pick 64/
N is No x (1/32) = ? for No = 64 that is 2.00
k from above.
Solve for t in years.
17190 years
To determine how long ago the plant was alive, we can use the fact that the half-life of Carbon-14 is 5730 years.
Since the fossil contains only 1/32.0 of the original amount of Carbon-14, it means that it has undergone 5 half-lives (since 2^5 = 32).
To find the elapsed time, multiply the half-life by the number of half-lives:
5730 years x 5 half-lives = 28,650 years.
Therefore, the plant was alive approximately 28,650 years ago.
To determine how long ago the plant was alive, we need to calculate the number of half-lives that have passed.
The given information tells us that the amount of Carbon-14 has decayed to 1/32.0 (or 1/2^5) of the original amount. This means that 5 half-lives have passed.
To find the time it takes for 1 half-life to pass, we use the given half-life value of 5730 years.
Time for 5 half-lives = 5 * 5730 years = 28650 years
Therefore, this plant fossil was alive approximately 28,650 years ago.