Question

A piece of charcoal is found to contain

Answer 1

Answer: The tree died 9709.46 years before.

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 = 100

a - x = amount left after decay process = $\frac{30}{100}\times 100=30$

a) to find rate constant

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

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

$k=\frac{0.693}{5600years}=1.24\times 10^{-4}years^{-1}$

b) to know the age

$t=\frac{2.303}{1.24\times 10^{-4}}\log\frac{100}{30}$

$t=9709.46years$

The tree died 9709.46 years before.