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MissPhiladelphia
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"The cloth shroud from around a mummy is found to have a 14C activity of 9.7 disintegrations per minute per gram of carbon as compared with living organisms that undergo 16.3 disintegrations per minute per gram of carbon. From the half-life for 14C decay, 5715 yr, calculate the age of the shroud. (Radioactive decay follows the first-order kinetics.) "

Solution:
[A]₀ = 16.3 dpm/g                    
[A]∨t = 9.7 dpm/g
t ∨1/2 = 5715 yr.
t=?

[A]₀ / [A]∨t = 16.3/9.7 = 2 ∧t/t ∨1/2
t/t∨1/2 = log 1.168/ log 2 = 0.225 / 0.301
           = 0.747
5715 years × 0.747 = 4270 years
Eduard22sly

The age of the shroud given that it contains 14C with a half-life of 5715 years is 4286 years

How to determine the number of half-lives

  • Original amount (N₀) = 16.3
  • Amount remaining (N) = 9.7
  • Number of half-lives (n) =?

2ⁿ = N₀ / N

2ⁿ = 16.3 / 9.7

2ⁿ = 1.68

Take the Log of both side

Log 2ⁿ = Log 1.68

nLog 2 = Log 1.68

Divide both side by Log 2

n = Log 1.68 / Log 2

n = 0.75

How to determine the age

  • Number of half-lives (n) = 0.75
  • Half-life (t½) = 5715 years
  • Time (t) =?

t = n × t½

t = 0.75 × 5715

t = 4286 years

Complete question

The cloth shroud from around a mummy is found to have a 14C activity of 9.7 disintegrations per minute per gram of carbon as compared with living organisms that undergo 16.3 disintegrations per minute per gram of carbon. From the half-life for 14C decay, 5715 yr, calculate the age of the shroud. (Radioactive decay follows the first-order kinetics.)

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