A rock contains 18 mg of the radioactive isotope carbon-14.The half-life of carbon-14 is 5,600 years.How many half-lives and years will it take before the carbon-14 decays to less than 4 mg?

Question

Quizplus · Accepted Answer

We can use the formula for exponential decay:

amount = initial amount x (1/2)^(number of half-lives)

Let's solve for the number of half-lives first:

4 mg = 18 mg x (1/2)^(number of half-lives)
(1/2)^(number of half-lives) = 4/18
(number of half-lives) = log(base 1/2) (4/18)
(number of half-lives) = 3.159

Rounding up gives us 4 half-lives.

To calculate the number of years:

1 half-life = 5,600 years 
4 half-lives = 4 x 5,600 = 22,400 years

Therefore, the answer is Choice C: 3 half-lives; 16,800 years.

A Rock Contains 18 Mg of the Radioactive Isotope Carbon-14