The Shroud of Turin is a rectangular linen cloth kept in the

The Shroud of Turin is a rectangular linen cloth kept in the Chapel of the Holy Shroud in the cathedral of St. John the Baptist in Turin, Italy. It shows the image of a man whose wounds correspond with the biblical accounts of the crucifixion. In 1389, Pierre d\'Arcis, the Bishop of Troyes, wrote a memo to the Pope, accusing a colleague of passing off \"a certain cloth, cunningly painted\" as the burial shroud of Jesus Christ. Despite this early testimony of forgery, the so-called Shroud of Turin has survived as a famous relic. In 1988, a small sample of the Shroud of Turin was taken and scientists from Oxford University, the University of Arizona, and the Swiss Federal Institute of Technology were permitted to test it. It was determined that 92.3% of the Shroud\'s original 14^C still remained. According to this information, how old was the Shroud in 1988? (Carbon-14 has a half-life of 5,730 years. Round your answer to the nearest year.) yr old The Arrhenius equation is used to relate the viscosity eta of a fluid (the fluid\'s internal friction, which is what makes it resist a tendency to flow) to its absolute temperature

Solution

Use the following expression:
C = Co exp(-kt)

k is a constant and can be determined by: k = ln2/t_1/2
k = ln2/5730 = 1.21x10^-4 yr^-1

It remains 92.3% of the original 14C so, this means that C = 0.923Co, hence:

0.923Co = Co exp(-1.21x10^-4t)
ln(0.923) = -1.21x10^-4t
-0.0801 = -1.21x10^-4t
t = 662.20 yr.

Hope this helps