Question

You find a fossil, and through careful study you find that only one-sixteenth of the carbon-14 that it once contained is still remaining in it. Carbon-14 has a half-life of approximately 5700 years. You can conclude that the age of the fossil is about __________.a. 4 × 5700 yr = 22,800 years
b. 16 × 5700 yr = 91,200 years
c. 1/16 × 5700 yr = 356 years
d. 5 × 5700 yr = 28,500 years

Answer 1

Answer:

The correct answer is:

5×5700 yr = 28,500 years (d)

Explanation:

The half life of an element/atom is the time is takes for that element/atom to decay to half of its original mass/size.

It was found that the carbon-14 atom had decayed until only $\frac{1}{16th}$ of the original size is still remaining.

Now, let us first find how many half lives are in one-sixteenth, and that is $\frac{1}{2}* \frac{1}{2}* \frac{1}{2}* \frac{1}{2}$ = $\frac{1}{16}$. so it means that there are 4 half lives in one-sixteenth, and since one half life takes approximately 5700 years, therefore 4 half lives will take 4×5700 yr = 22, 800 years, but at this point (22,800 years ago)the fossil has already half-life, therefore the additional age is to add the number of years it took to decay that half life. hence the age of fossil is:

22,800 + 5700 = 28, 500 years