(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?
a) 10/12 = (1/2)^(t/5700)
[log(10/12)] / log(1/2) = t / 5700
b) use t from a)
c = 12 * (1/2)^[(t+100)/5700]
c / 12 = (1/2)^[(t+100)/5700]
To determine the age of the fossil, we can use the concept of half-life of Carbon-14.
(a) The half-life of Carbon-14 is 5700 years, which means that every 5700 years, half of the Carbon-14 decays into Nitrogen-14.
In this case, we know that the fossil currently contains 10 grams of Carbon-14, and it originally had 12 grams when it died.
Since the half-life of Carbon-14 is 5700 years, it means that every 5700 years, half of the Carbon-14 decays. So, if the current amount is 10 grams, we can determine the number of half-lives it went through.
10 grams is half of 12 grams, so we can conclude that the fossil went through 1 half-life.
Now, we can calculate the age of the fossil by multiplying the half-life by the number of half-lives.
5700 years * 1 half-life = 5700 years.
Therefore, the age of the fossil is estimated to be 5700 years.
(b) To determine how much Carbon-14 will be present in the sample 100 years from now, we need to calculate the number of half-lives that will occur in 100 years.
Since the half-life of Carbon-14 is 5700 years, we can divide 100 years by 5700 years to find the number of half-lives.
100 years / 5700 years = approximately 0.0175 half-lives.
Since half-life is not a continuous process, we round this number to the nearest whole number. Therefore, there will be 0 half-lives occurred in 100 years.
Since no half-lives have occurred, the amount of Carbon-14 will remain the same in the sample. Therefore, the amount of Carbon-14 present in the sample 100 years from now will be the same as it is currently, which is 10 grams.