(a) Find the age of the sample, assuming that the activity per gram of carbon in

Question

(a) Find the age of the sample, assuming that the activity per gram of carbon in a living organism has been constant at a value of 0.23 Bq.

(b) Evidence suggests that the value of 0.23 Bq might have been as much as 38% larger. Repeat part (a), taking into account this 38% increase.

Units plz!!!!

A sample has a activity of 0.0049 Bq per gram of carbon. Find the age of the sample, assuming that the activity per gram of carbon in a living organism has been constant at a value of 0.23 Bq. Evidence suggests that the value of 0.23 Bq might have been as much as 38% larger. Repeat part (a), taking into account this 38% increase.

Explanation / Answer

the relation between intitial and final activities and time elapsed is given by the formula

A2 = A1(2^(-t/h)) (h = half-life)

a)

half life of carbon 14 in 5730 years.

so applying the formula

0.0049 = 0.23(2^(-t/h))

log(0.0049/0.23)/log2 = -t/h

-5.55 = -t/5730

t = 5730*5.55 = 31817 years.

b)

if the original sample had a 38% higher activity.

= 0.23*138/100 = 0.317

new age of sample would be 5730* log(0.0049/0.317)/log2 = 34469 years

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