(Carbon-14 dating) Living plant material contains a constant specific activity of…

CHEMISTRY · Subjective · US High School · Chemistry · Atomic Structure & Nuclear · Atomic Structure & Nuclear

Problem

(Carbon-14 dating) Living plant material contains a constant specific activity

A_0

of carbon-14. A fragment of ancient wood is analysed and its present specific activity is found to be

A

(

A < A_0

). The half-life of

^{14}

C is 5730 years. (i) Starting from the law of radioactive decay, derive an expression for the age

t

of the wood in terms of

A

A_0

and the decay constant

\lambda

. (ii) For a particular specimen,

A = 12

disintegrations min

^{-1}

^{-1}

while

A_0 = 16

disintegrations min

^{-1}

^{-1}

. Calculate the age of the specimen. (iii) Determine the percentage of the original

^{14}

C nuclei that remain undecayed in the specimen today.