A plant fossil lost 40 % of its carbon-14. How old is the fossil? (Half-life of carbon-14 is 5730 years.)
To determine the age of the fossil, we can use the concept of half-life of carbon-14.
Carbon-14 is an isotope that is commonly used for dating organic samples, such as plant fossils. It has a half-life of 5730 years, meaning that after 5730 years, half of the carbon-14 in a sample will have decayed.
In this case, we are given that the plant fossil has lost 40% of its carbon-14. To determine the age, we need to figure out how many half-lives it took for the carbon-14 to reduce by 40%.
Let's start by calculating the number of half-lives:
40% = 40/100 = 2/5
Now, we need to find the number of half-lives it took to reduce the carbon-14 to 2/5 (40%).
To find the number of half-lives, we can use the formula:
Number of half-lives = (log(remaining amount/initial amount))/(log(1/2))
In this case, the remaining amount is 2/5 (40%), and the initial amount is 1 (100%).
Number of half-lives = (log(2/5))/(log(1/2))
Using logarithmic values, we can calculate:
Number of half-lives ≈ 0.3010 / (-0.3010)
Number of half-lives ≈ -1
Since we cannot have a negative number of half-lives, we need to take the absolute value to obtain a positive result.
Number of half-lives ≈ 1
Therefore, it took approximately 1 half-life for the plant fossil to lose 40% of its carbon-14.
Now, to determine the age of the fossil, we need to multiply the number of half-lives by the half-life of carbon-14:
Age of the fossil = Number of half-lives * Half-life
Age of the fossil ≈ 1 * 5730 years
Age of the fossil ≈ 5730 years
Hence, the fossil is approximately 5730 years old.