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_{(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.