Question

Anthropologists can estimate the age of a bone or other sample of organic matter by its carbon-14 content. The carbon-14 in a living organism is constant until the organism dies, after which carbon-14 decays with first-order kinetics and a half-life of 5730 years. Suppose a bone from an ancient human contains 14.0 %% of the CC-14 found in living organisms.

Answer 1

Answer: The age of a bone or other sample of organic matter by its carbon-14 content is 16252 years

Explanation:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process  

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

$t_{\frac{1}{2}}=\frac{0.693}{k}$

$k=\frac{0.693}{5730}=1.21\times 10^{-4}years^{-1}$

b) for completion of 14 % of reaction

$t=\frac{2.303}{k}\log\frac{100}{14}$

$t=\frac{2.303}{1.21\times 10^{-4}}\log\frac{100}{14}$

$t=16252years$

The age of a bone or other sample of organic matter by its carbon-14 content is 16252 years