The bones of a saber-toothed tiger are found to have an activity per gram of carbon that is 30.0% of what would be found in a similar live animal. How old are these bones?
SOLUTION :
Radioactive carbon 14C has half-life of 5730 years.
So,
A / A0 = e^(- lamda * t)
=> 1/2 = e^(- lamda * 5730)
Taking ln :
=> ln(1/2) = - lamda * 5730
=> lamda = - ln(1/2) / 5730 = 1.20968 * 10^(-4)
So,
A(now) / A0 = e^(- 1.20968*10^(-4) * t)
=> 0.30 = e^(- 1.20968*10^(-4) * t)
Takin ln :
=> ln(0.30) = - 1.20968*10^9-4) * t
=> t = ln(0.30) / (- 1.20968*10^(-4)
=> t = 9952.82 years
Hence, the bones are 9952.82 years old (ANSWER)
The bones of a saber-toothed tiger are found to have an activity per gram of carbon...
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