Question

A fossilized leaf contains 18% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14 13,829 1600 35,538 23,309

Answer 1

Answer: The age of the fossilized leaf is 13829 years.

Step-by-step 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 = $\frac{18}{100}\times 100=18$  

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.

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

$k=\frac{0.693}{5600years}=0.00012years^{-1}$

b) for finding the age

$t=\frac{2.303}{0.00012}\log\frac{100}{18}$  

$t=13829years$

The age of the fossilized leaf is 13829 years.