Question

Planks from an old boat were found in a cave near the shore. Analysis of the boat's wood gave 13.6 disintegrations/min/g of carbon. The half-life of C-14 is 5730 years. Analysis of a tree cut down when the cave was found showed 15.3 disintegrations/min/g of C-14. In what century was the boat built?

Answer 1

Ratio = 13.6 dis/mingC / 15.3 dis/mingC

Ratio = 0.88888

The ratio is equal to

Ratio = 2^{(t / t_1/2)}

log(Ratio) = -(t / t_1/2) * log2

t = -t_1/2 x log(Ratio) / log2
t = -5730yr x log 0.8888 / log2
t = -5730yr x (-0.05115) / 0.3010
t = 973 years old

The year 1043 it was built. Hence it is about 11^th centuary