A rare find of carbon containing soft tissue (biological tissue, such as protein

Question

A rare find of carbon containing soft tissue (biological tissue, such as proteins) in a T-rex dinosaur fossil bone that is thought to be 65 million years old has recently been discovered by paleontologist Mary Schweitzer. You have been asked to analyze a sample of the tissue for carbon-14 dating. The activity of the sample was found to be 8 x 10-5 disintegrations per second. An equal mass of fresh sample of human tissue was found to be 15.200 disintegrations per second. The half-life of carbon-14 is 5700 yr. Calculate the age of the dinosaur tissue from the data you acquired.

Explanation / Answer

t1/2 = 5700 years

C = Co exp(-kt)

Ln(2) = k * t1/2 = 0.693

k = 0.000122 yr-1

Activity of sample, A = C * k = 8 x 10-5 dis/sec

Activity of fresh sample, Ao = Co * k = 15.2 dis/sec

C = A / k

Co = Ao/k

C / Co = A / Ao = 5.26 x 10-6

C / Co = exp(-kt)

5.26 x 10-6 = exp(-0.000122 t)

0.000122 t = 12.155

Age of dinosaur tissue, t = 99953 years

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