A molar from a mammoth skeleton is dated using a measurement of its^14C content.

Question

A molar from a mammoth skeleton is dated using a measurement of its^14C content. Carbon from the tooth is chemically extracted and formed into benzene. The benzene sample is placed in a shielded chamber. Beta decays from the carbon in the sample come at an average rate of 12 counts per minute. A sample produced from a modern elephant molar in exactly the same way gives a count rate of 54 counts per minute. What is the asge of the skeleton? Assume a^14C half life of 5700 years. Show your work and explain your reasoning.

Explanation / Answer

Here ,

final activity , A = 12 counts/min

initial activity , A0 = 54 counts/min

half life of C-12 , t0.5 = 5730 years

for the age of the mammoth

A = A0 * 0.5^(t/t0.5)

12 = 54 * 0.5^(t/5730)

solving for t

t = 12433.7 years

the age of the mammoth is 12433.7 years

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