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

Answer:

t = 26541.55 years

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 $\lambda = \frac{0.693}{5730}$

we know $A ' = A e^{-\lambda t}$

$5.76*10^2 = 0.94 * 15 * 1000 e^{-\frac{0.693}{5730}t}$

$0.040 = e^{-\frac{0.693}{5730}t}$

taking log on both side

$-3.21 = -\frac{0.693}{5730}t$

t = 26541.55 years