Question

A piece of charcoal used for cooking is found at the remains of an ancient campsite. A 0.96-kg sample of carbon from the wood has an activity equal to 5.76 ✕ 10^2 decays per minute. Find the age of the charcoal. Hint: Living material has an activity of 15.0 decays/minute per gram of carbon present. yr

Answer 1

t = 26541.55 years

Step-by-step explanation:

let the age of charcoal is t

Activity of living material = 15 decays / min /g

Activity of living material = 15 * 1000 decays /min /kg

Acitivity of living material per 0.94 kg A = 0.94 *15 * 1000 decays / min

Activity of after time t is A ' = 5.76*10^2 decay per minute

half life of carbon = 5730 years

designtegration constant
`\lambda = (0.693)/(5730)`

we know
`A ' = A e^(-\lambda t)`

`5.76*10^2 = 0.94 * 15 * 1000 e^{-(0.693)/(5730)</p><p>t}`

`0.040 =  e^{-(0.693)/(5730)t}`

taking log on both side

`-3.21 = -(0.693)/(5730)t`

t = 26541.55 years