Answer to Question #315618 in Inorganic Chemistry for pulsne

Question

A cache of Hebrew manuscripts known as the Dead Sea Scroll was found in 1947. The

specific activity of Carbon-14 in the linen wrappings of the book of Isaiah was about

0.200 disintegration per second per gram (dps g-1.). Carbon-14 in living materials has

a specific activity of 0.255 dps g-1. The half-life of Carbon-14 is

5.73 x103 years. Carbon-14 decay by First order rate law. Calculate the approximate

age of the linen

Answer 1

"Half life" means the amount of time that elapses before 1/2 = 50% of the amount of carbon 14 has disappeared. The rate of decay is 5730 years. Let the start mass be A₀ at the first year.

The decay rate is geometric, i.e.

-1.20968•10^-4 × t = ln(0.7)

t = 2948.5 years