# From the half-life for 14C decay, 5715 years, calculate the age of the shroud?

The cloth shroud from around a mummy is found to have a 14C activity of 9.5 disintegrations per minute per gram of carbon as compared with living organisms that undergo 15.2 disintegrations per minute per gram of carbon.

Question: From the half-life for 14C decay, which is 5715 years, calculate the age of the shroud.

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Please help with this problem. I have no idea where to begin.

### 4 Answers

- HPVLv 71 decade agoFavorite Answer
You need two equations to solve this problem.

t 1/2 = 0.693 / k and

ln (Nt / No) = -kt . . .where Nt / No is the ratio of radioactive nuclei at time t compared to the original number of nuclei. This is proportional to the number of disintegrations at time t versus the original number of disintegrations.

t 1/2 = 0.693 / k

k = 0.693 / t 1/2 = 0.693 / 5715 yr = 1.21 x 10^-4 yr^-1

ln (Nt / No) = -kt

ln (9.5 / 15.2) = -(1.21 x 10^-4) t

-0.47 = -1.21 x 10^-4 t

3880 yr = t = age of shroud

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- 4 years ago
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RE:

From the half-life for 14C decay, 5715 years, calculate the age of the shroud?

The cloth shroud from around a mummy is found to have a 14C activity of 9.5 disintegrations per minute per gram of carbon as compared with living organisms that undergo 15.2 disintegrations per minute per gram of carbon.

Question: From the half-life for 14C decay, which is 5715 years, calculate...

Source(s): life 14c decay 5715 years calculate age shroud: https://shortly.im/lOsT0- Login to reply the answers

- 6 years ago
9.5/15.2=.625 or 62.5%.

So the disintegrations are 62.5% of that of living organisms.

.5^x=.625 ==> x=(ln.625/ln.5)= .678 half lives.

multiply .678 half lives by 5715 (the half life of carbon 14)= 3875 or 3.9*10^3 years

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