If C14 has a half-life of 4,000 years, what fraction will be remaining after 36,000 years?

See you I-131 post. Same procedure.

To determine the fraction of C14 remaining after 36,000 years, we can use the half-life concept. The half-life of an element is the time it takes for half of the substance to decay.

In this case, the half-life of C14 is given as 4,000 years. This means that after 4,000 years, half of the C14 would have decayed, and only half would remain.

To find the fraction that remains after 36,000 years, we need to determine how many half-lives have passed. Since the half-life is 4,000 years, we can divide the total time (36,000 years) by the half-life:

Number of half-lives = Total time / Half-life
Number of half-lives = 36,000 years / 4,000 years
Number of half-lives = 9

So, after 36,000 years, 9 half-lives of C14 have occurred. Each half-life reduces the amount of C14 by half.

Now, we can calculate the fraction remaining by raising 1/2 to the power of the number of half-lives:

Fraction remaining = (1/2)^(Number of half-lives)
Fraction remaining = (1/2)^9
Fraction remaining = 1/512

Therefore, after 36,000 years, approximately 1/512 (or around 0.002) of the original C14 will remain.