Apiece of charcoal used for cooking is found at the remains of an ancient campsite. a 0.94 kg sample of carbon from the wood has an activity of 1580 decays per minute. find the age of the charcoal. living material has an activity of 15 decays/minute per gram of carbon present and the half-life of 14c is 5730 y. answer

Mass of sample of charcoal = 0.94 kg = 0.00094 

∴, activity = decay rate / mass = 1580/0.00094
                                                 = 1.681 X 10^6 decays per min per gram

Using the half-life formula, we have: 
activity of sample / activity of modern carbon = (1/2)^(age / half-life) 
∴, Age = half-life x log (base 2) (modern activity / coal activity)
           = 5730 x log(base 2)(1.681X10^6/ 15)
           = 96115 years.

Age of the charcoal = 96115 years

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