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A fossilized bone is found to contain 0.1% of its original amount of C-14. Determine the age of the fossil.

A fossilized bone is found to contain 0.1% of its original amount of C-14. Determine the age of the fossil.

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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EXAMPLE Age of a Fossil A fossilized bone is found to contain 0.1% of its original amount of C-14. Determine the age of the fossil. SOLUTION The starting point is again A(t) = Aoekt. To determine the value of the decay constant k we use the fact that Ao = A(5730) or Ao = Age 5730k. The last equation implies 5730k = In-In2 and so we get k = -(In2)/5730 = -0.00012097. Therefore A(t) = Age-0.00012097, With A(t) = 0.001Ao we have 0.001A0 = Age-0.000120971 and -0.00012097t=In(0.001) -In 1000. Thus = t= In 1000 0.00012097 57,100 years.
Transcribed Image Text:EXAMPLE Age of a Fossil A fossilized bone is found to contain 0.1% of its original amount of C-14. Determine the age of the fossil. SOLUTION The starting point is again A(t) = Aoekt. To determine the value of the decay constant k we use the fact that Ao = A(5730) or Ao = Age 5730k. The last equation implies 5730k = In-In2 and so we get k = -(In2)/5730 = -0.00012097. Therefore A(t) = Age-0.00012097, With A(t) = 0.001Ao we have 0.001A0 = Age-0.000120971 and -0.00012097t=In(0.001) -In 1000. Thus = t= In 1000 0.00012097 57,100 years.
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