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Question

An archaeologist finds a piece of old bone that she believes may be 2000 years old. The lab technician tells her that the carbon-14 in the bone has completed 25 percent of its first half-life. One-half life for the element carbon-14 takes 5730 years. Does this finding support her belief about the age of the bone? Why or why not?

A paleontologist unearths the remains of a Tyrannosaurus rex. We know that these dinosaurs became extinct about 65 million years ago. Therefore, would it be reasonable to expect that the carbon-14 in the fossil has completed 15000 half-lives? Why or why not? Again, one half-life for the element carbon-14 takes 5730 years.

Answer 1

25% of 5730 is 1432, which is reasonably close to 2000; i'm not sure how accurate they want to be.

As to the latter: 15000 half-lives almost certainly means that all of the carbon-14 would have decayed. 0.5^15000 is a vanishingly small number; if this was the fraction of remaining carbon-14 atoms in a sample, it would certainly suggest that far fewer than one (i.e., zero) carbon-14 atoms should remain.

Answer 2

The decay formula is M(t) = M0*e^-t*(ln2)/th where th is the half life and M0 the initial mass of C14.

(Put t=th in this formula and you will see that M(th) = e^-ln2= 1/e^ln2 = 1/2)

You are given that th = 5730 yrs. Putting the numbers in, you get
M(2000yr) = 0.785M0, which does support the finding that 25% is decayed. (75% is left)

If t = 15000th, then M(t)/M(0) = e^-15000*ln(2), an extremely small number, so essentially no carbon 14 is left.

Answer 3

carbon 14 in a fossil used for dating things such as bones up to about 50,000 years old so you should be able to solve the problem from this figure.

Answer 4

the carbon would be 2865 years old. it would have been 11343.8045 have lives

Answer 5

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