Carbon-14 has a half-life of 5730 years In a plant fossil you find that the 14 C has decayed to 1/8 of the original amount how long ago was this plant
To find out how long ago the plant fossil formed, we need to use the concept of radioactive decay and the half-life of carbon-14.
The half-life of carbon-14 is 5730 years, which means that after 5730 years, half of the original carbon-14 atoms in a sample would decay. In this case, we know that the carbon-14 has decayed to 1/8 of the original amount.
So, to determine the elapsed time, we need to figure out how many half-lives it took for the carbon-14 to decay to 1/8 of the original amount.
1/8 can be expressed as 1/2^3, where 3 is the number of half-lives. This means that three half-lives have passed since the plant fossil formed.
To find the time, we multiply the half-life by the number of half-lives: 5730 years × 3 half-lives = 17190 years.
Therefore, the plant fossil formed approximately 17190 years ago.
1/8=e^-.693t/5630
4730 ln(1/8)=-.693t
solve for t
another way:
1/8=(1/2)^t
t=3 halflives