Carbon-14 has a radioactive half-life of 5730 years. If an organism has 10 g of carbon-14 remaining in its body from a sample that originally had 80 grams in its body, how old is the organism?

Answer 1

Simply use FR = 0.5ⁿ

FR = fraction remaining

n = number of half lives that have elapsed

FR = 10 g/ 80 g = 0.125

Solve for n:

0.125 = 0.5ⁿ

log 0.125 = log 0.5 n

n = 3 half lives have elapsed

Each half life = 5730 years, so age of object is...

3 half lives x 5730 yrs/half life = 17,192 years old

Answer 2

The radioactive half-life describes how long it takes to HALVE the amount of radioactive substance per every X number of years--in this problem, that's 5730. And in this question, they give you the END amount of radioactive substance and ask how old the sample is--and so, to answer it, you go backwards. DOUBLE the grams per every 5730 years and count how many times you double it until you reach 80. So:

10g --> 20g, 5730 years.

20g--> 40g, 5730 years.

40g--> 80g, 5730 years.

5730+5730+5730 = 17,190 years.