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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

Respuesta :

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 [tex]\lambda = \frac{0.693}{5730}[/tex]

we know [tex]A ' = A e^{-\lambda t}[/tex]

[tex] 5.76*10^2 = 0.94 * 15 * 1000 e^{-\frac{0.693}{5730}

t}[/tex]

[tex]0.040 =  e^{-\frac{0.693}{5730}t}[/tex]

taking log on both side

[tex]-3.21 = -\frac{0.693}{5730}t[/tex]

t = 26541.55 years

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