An archaeologist finds the ¹⁴C in a sample of $2.10 \mathrm {~g}$ of material to be decaying at 107 Bq. A modern $1.00 - \mathrm { g }$ sample of the same material decays at 151 Bq,and assume this rate has also held in the past. The half-life of ¹⁴C is 5730 years. How old is the sample?

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The decay rate of the sample is 107 Bq for 2.10 g, which is equivalent to 51 Bq/g. The modern sample decays at 151 Bq/g. Using the decay formula and the half-life of 5730 years, the age of the sample is calculated to be approximately 8980 years.

An Archaeologist Finds the 14C in a Sample Of 2.10 g2.10 \mathrm {~g}2.10 g

An Archaeologist Finds the ¹⁴C in a Sample Of $2.10 \mathrm {~g}$