From the half-life for 14c decay, 5715 yr, calculate the age of the shroud.

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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