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.

Question

asked Oct 9, 2018 151k views

2 Answers

Jevaughn · Answer 1 · 2018-10-14T02:52:17+0000

Answer: 90.2 days

Explanation:-

Radioactive decay follows first order kinetics.

Half-life of Iron-59 = 45.1 days

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

$N=N_o* e^(-\lambda t)$

N = amount left after time t=
(25)/(100)* a=0.25a

N_0 = initial amount = a

$\lambda$ = rate constant=
0.015 days^(-1)

t= time = ?

$0.25a=a* e^{- 0.0153 years^(-1)* t days}$

t=90.2days

Thus the iron sample is 90.2 years old.