In a living organism, the decay of C-14 produces 15.3 disintegrations per minute

Question

In a living organism, the decay of C-14 produces 15.3 disintegrations per minute per gram of carbon. The half-life of C-14 is 5730 years. A bone sample with 3.5 g of carbon has 38.4 disintegrations per minute. The bone sample is found to be 2749 years old. What percentage of the atoms of carbon in the biosphere are C-14?

HINT: (want the number of C-14 atoms in 1 g)/(total C atoms in 1 g)x100%. Use rate = kN for number of C-14 and what you know about moles and Avogadro's number for the total number of C atoms in 1 g.

Explanation / Answer

15.3 D/min per gram

HL = 5730 years

M0 = 3.5 g of carbon

C = 38.4 d/min

t = 2749 years...

find C0

a)

first, identify a basis such as " 1 gram"

so...

38.4 D/min / 3.5 = 10.97142 disintegrations/min

compare rates:

Cfinal = C0*(1/2)^(t/HL)

10.97142 = C0*(1/2)^(2749/5730 )

solve for C0

C0 = 10.97142 / ((1/2)^(2749/5730 ))

C0 = 15.299 desinterations per minute (in 1 gram of sample)

15.3 carbon atoms pe rminute in the sample of C-14

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