Question

Wood deposits recovered from an archaeological site contain 36% of the C-14 they originally contained. How long ago did the tree from which the wood was obtained die?

Answer 1

Answer: It was obtained 8515 years ago

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) to find the rate constant:

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

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

$k=\frac{0.693}{5760}=0.00012years^{-1}$

b) for completion of 36% of reaction

$t=\frac{2.303}{k}\log\frac{100}{36}$

$t=\frac{2.303}{0.00012}\log\frac{100}{36}$

t = 8515 years

The time was 8515 years.