Question

A piece of charcoal used for cooking is found at the remains of an ancient campsite. A 1.09 kg sample of carbon from the wood has an activity of 2020 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 in units of y.

Answer 1

t = 17199 years

Step-by-step explanation:

given,

mass of sample = 1.09 Kg

Activity of living material = 15 decays / min /g

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

Activity of living material per 1.09 kg A = 1.09 x 15 x 1000 decays / min

Activity of after time t is A ' = 2020

half life = 57300 years

desegregation constant

λ = 0.693 / 5700

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

`A'= 1.09 * 15 * 1000 e^(-\lambda\ t)`

`2020= 1.09 * 15 * 1000 e^{-(0.693)/(5700)* t}`

`0.124=e^{-(0.693)/(5700)* t}`

taking ln both side

`(0.693)/(5700)* t = 2.09`

t = 17199 years