Q1. If a tree dies and the trunk remains undisturbed for 13,750 years, what percentage of the original 14C is still present? (The half-life of 14C is 5730 years.)
a. 2.20%
b. 45.0%
c. 19.0%
d. 5.20%
(1/2)^(13750/5730) = 0.1895
Well, it sounds like that tree has really been "stuck in a tree-rut" for a while! To figure out the percentage of original 14C remaining, we can use the half-life of 5730 years.
Now, if 5730 years is the half-life, then after 5730 years, half of the original 14C would remain. So after 13,750 years, let's think about it.
After the first 5730 years (one half-life), we're left with half of the 14C. After the next 5730 years (another half-life), we're then left with just one-fourth of the original 14C. And if we repeat that process for another 5730 years (another half-life), we're then left with one-eighth of the original 14C.
Now, doing a little math, we can calculate that after 13,750 years, approximately 5.20% of the original 14C is still around. So the answer is d. 5.20%. Looks like that tree has been playing "hide and seek" with its carbon atoms!
To calculate the percentage of the original 14C that is still present after 13,750 years, we need to determine the number of half-lives that have passed.
The half-life of 14C is 5730 years. Therefore, to find the number of half-lives that have passed, we divide the total time by the half-life:
Number of half-lives = Total time / Half-life
Number of half-lives = 13,750 years / 5730 years
Now, calculating the number of half-lives:
Number of half-lives = 2.397
To find the percentage of 14C remaining after 13,750 years, we use the formula:
Percentage remaining = (1/2)^(Number of half-lives) * 100
Percentage remaining = (1/2)^(2.397) * 100
Calculating the percentage remaining:
Percentage remaining = 0.192 * 100
Percentage remaining = 19.2%
Therefore, the answer is c. 19.0%.
To find the percentage of the original 14C that is still present after 13,750 years, we need to use the concept of half-life.
The half-life of 14C is 5730 years. This means that after 5730 years, half of the original 14C will have decayed. Then, after another 5730 years, half of the remaining 14C will decay, and so on.
First, we calculate how many half-lives have elapsed in 13,750 years:
number of half-lives = (elapsed time) / (half-life) = 13750 / 5730 = 2.4 approximately
Since we can't have a fraction of a half-life, we round to the nearest whole number. In this case, 2 half-lives have elapsed.
Now, we can calculate the percentage of the original 14C that is still present:
percentage = (1/2)^(number of half-lives) * 100
= (1/2)^(2) * 100
= 1/4 * 100
= 25%
Therefore, 25% of the original 14C is still present after 13,750 years.
None of the given answer options match the calculated result of 25%.