Answer to Question #316552 in Inorganic Chemistry for Shula Kapembwa

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

Solution:

The half-life (t_1/2) of carbon-14 is 5.73×10³ years

From law of radioactive decay:

t_1/2 = ln(2) / λ

where λ = decay constant

λ = ln(2) / t_1/2

λ = (0.693) / (5.73×10³ years) = 1.21×10⁻⁴ years⁻¹

Radioactive decay follows the kinetics of a first order reaction:

ln(a) = −λt + ln(a_o)

The specific activity of carbon-14 in the linen wrappings of the book = a = 0.200 dps g⁻¹

The specific activity of carbon-14 in living materials = a_o = 0.255 dps g⁻¹

Therefore,

ln(0.200) = − (1.21×10⁻⁴) × t + ln(0.255)

−1.609438 = − (1.21×10⁻⁴) × t + (−1.366492)

(1.21×10⁻⁴) × t = 0.242946

t = (0.242946) / (1.21×10⁻⁴) = 2007.8

t = 2007.8 years

Answer: The approximate age of the linen is 2007.8 years