(a)-A fossilised tree was tested and contains 10 grams of Carbon-14. Given that there was 12 grams of Carbon-14 present when it died, determine the age of the fossil? Half life of Carbon-14 is 5700 years.
(b)How much Carbon-14 will be present in the sample 100 years from now?
If possible all working in understandable format, Cheers
(a) 12(1/2)^(t/5700) = 10
t = 1499.3 years
(b) 12(1/2)^(1599.3/5700) = 9.879 grams
(a) To determine the age of the fossil, we need to use the concept of half-life. The half-life of Carbon-14 is given as 5700 years, which means every 5700 years, the amount of Carbon-14 in a sample will decrease by half.
We can calculate the number of half-lives that have occurred by taking the amount of Carbon-14 in the fossil (10 grams) and dividing it by the initial amount of Carbon-14 (12 grams).
10 grams / 12 grams = 0.8333
Now, we need to find the age of the fossil by multiplying the number of half-lives by the length of one half-life.
0.8333 x 5700 years = 4749.99 years
Rounding to the nearest whole number, the age of the fossil is approximately 4750 years.
(b) To calculate the amount of Carbon-14 in the sample 100 years from now, we need to determine the number of half-lives that will occur in that time.
First, calculate the number of half-lives by dividing 100 years by the length of one half-life (5700 years).
100 years / 5700 years = 0.0175
Next, calculate the remaining fraction of Carbon-14 by subtracting the number of half-lives from 1.
1 - 0.0175 = 0.9825
Finally, multiply the remaining fraction by the initial amount of Carbon-14 (12 grams) to find the amount of Carbon-14 that will be present in the sample 100 years from now.
0.9825 x 12 grams = 11.79 grams
Therefore, approximately 11.79 grams of Carbon-14 will be present in the sample 100 years from now.