Question

Iron-59 has a half-life of 45.1 days. how old is an iron nail if the fe-59 content is 25% that of a new sample of iron? show all calculations leading to a solution.

Answer 1

I have attached a paper with the answer. hope you understand. let me know if you have any question

Answer 2

Answer: 90.2 days

Explanation:-

Radioactive decay follows first order kinetics.

Half-life of Iron-59 = 45.1 days

$\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{45.1}= 0.0153 days^{-1}$

$N=N_o\times e^{-\lambda t}$

N = amount left after time t= $\frac{25}{100}\times a=0.25a$

$N_0$ = initial amount  = a

$\lambda$ = rate constant= $0.015 days^{-1}$

t= time  = ?

$0.25a=a\times e^{- 0.0153 years^{-1}\times t days}$

$t=90.2days$

Thus the iron sample is 90.2 years old.