You are assisting in an anthropology lab over the summer by carrying out 14C dat

Question

You are assisting in an anthropology lab over the summer by carrying out 14C dating. A graduate student found a bone he believes to be 20,000 years old. You extract the carbon from the bone and prepare an equal-mass sample of carbon from modern organic material. To determine the activity of a sample with the accuracy your supervisor demands, you need to measure the time it takes for 12,000 decays to occur.

A) The activity of the modern sample is 1.08 Bq . How long does that measurement take?

B) It turns out that the graduate student's estimate of the bone's age was accurate. How long does it take to measure the activity of the ancient carbon?

Explanation / Answer

Solution:- (A) 1 Bq = 1 disintegration/second

so, 1.08 Bq = 1.08 disintegrations/second

12000 disintegrations x (1 second/1.08 disintegration) = 11111.11 seconds or 185 min.

(B) we know that, ln[A] = - kt + ln[A]0

half life for carbon isotope is 5730 years.

we know that, k = 0.693/half life = 0.693/5730y = 1.21 x 10-4 y-1

[A]0 is 1.08 Bq, t = 20000y, k = 1.21 x 10-4 y-1, [A] = ?

plugging in the values..

ln[A] = - 1.21 x 10-4 y-1 x 20000y + ln(1.08)

ln[A] = -2.42 + 0.07696

ln[A] = -2.34304

[A] = 0.0960 Bq

Now we could solve this same as we solved part A.

12000 disintegrations x (1 second/0.0960 disintegrations) = 125000 second or 34.7 hours.

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