Question

How old is a sample of wood whose 14C content is found to be 43% that of a living tree? The half-life of 14C is 5730 years.

(b) Iodine-131 is one of the most important isotopes used in the diagnosis of thyroid cancer. One atom has a mass of 130.906114 amu. Calculate the binding energy per nucleon. 

Answer 1

Decay constant  $=\frac{0.693}{t\frac{1}{2}}= \frac{0.693}{5730years}= 1.209×10^{-4}/years$

The rate of counts is proportional to the number of C-14 atoms in the sample.

$N_0​=100,$

$N=43$

The age of the sample $=t=\frac{2.303}{k}​log[\frac{N_0}{N}]$

$t=\frac{2.303}{1.209×10^{-4}}×​log[\frac{100}{43}]=$ 4430 years

Binding energy per nucleon. 

$=\frac{1.184481amu.\frac{931Mev}{1amu}}{131}=8.422Mev/nucleons$