Question #123976
Living matter has an activity of 260 Bq/kg due to carbon – 14. If a sample of wood from a
burial site has an activity of 155 Bq/kg, estimate the age of the site. (Assume the half – life
of carbon – 14 is 5730 years).
1
Expert's answer
2020-06-30T18:26:42-0400

 The activity of the wood decreases as:


At=A0(12)thA_t=A_0(\frac{1}{2})^\frac{t}{h}T12=5730T_\frac{1}{2}=5730

A0=260bq/kgA_0=260bq/kg

A=155dq-Activity at the time T

Therefore;

A=00(TT12T=T12log2[A0A]A=0_0(−\frac{T}{T}\frac{​1}{2}→T=T_\frac{1}{2}log_2[A_\frac{0}{A}]

5730×log2[260155=4276years5730\times log_2[\frac{260}{155}=4276years

Therefore the age of the site is 4276 years.



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