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## Homework Statement

The carbon in living matter contains fixed proportion of the radioactive isotope carbon-14. The carbon-14 in 1.00g of living matter has an activity of 0.250Bq. The half life of carbon-14 is 5730 years.

(a) Calculate (i) The decay constant in s

^{-1}(ii) the number of carbon-14 atoms required to produce an activity of 0.250Bq.

(b) When a plant dies the proportion of carbon-14 decreases due to radioactive decay. A 1.00g sample of carbon from an ancient boat has an activity of 0.0625Bq. Determine the age of the boat.

## Homework Equations

A = yN

A = A

_{0}e

^{-yt}

A

_{0}= yN

_{0}

A = A

_{0}e

^{-yt}

## The Attempt at a Solution

I've worked out (a) (i) to be 2.48x10

^{-12}and (ii) N = 1.01x10

^{11}

I don't know how to work out (iii) because I don't know how to work out N

_{0}or A

_{0}. I found using A = yN --> N = A/y = 2.52x10

^{10}

How to find either A

_{0}or N

_{0}so that I can use A = A

_{0}e

^{-yt}or N = N = N

_{0}e

^{-yt}?