You find a fossil, and through careful study you find that only one-sixteenth of the carbon-14 that it once contained is still

2 answers
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

Answers

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 [tex]\frac{1}{16th}[/tex] of the original size is still remaining.

Now, let us first find how many half lives are in one-sixteenth, and that is [tex]\frac{1}{2}* \frac{1}{2}* \frac{1}{2}* \frac{1}{2}[/tex] = [tex]\frac{1}{16}[/tex]. 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

The answer is: A) 4 × 5,700 years = 22,800 years

Explanation:

Each half-life of Carbon-14 is approximately 5,700 years.

The amounts of Carbon-14 remaining in a specimen sample are:

After one half life only half of the original Carbon-14 amount remains. After two half lives only one fourth of the original Carbon-14 amount remains. After three half lives only one eight of the original Carbon-14 amount remains. After four half lives only sixteenth of the original Carbon-14 amount remains.

Since only one sixteenth of the original Carbon-14 remained, we can conclude that the fossil is four half lives old.

All we do now is multiply 4 x 5,700 years (half life of Carbon-14) = 22,800 years

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