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

Is this how you would do this?
(100/25) = 0.693 times (45.1)
4= 31.2543
final answer is 7.8136

Answer 1

25=100 e^(-.693 t/45.1)

take the ln of each side...

Ln(25)=ln(100) -.693 t/45.1
ln(25)-ln(100)=-.693 t/45.1
ln(25/100)=-.693t/45.1

t= - 45.1/.693 ( ln .25)

putting that into the goggle calculator..

t=90.2 days.

Now the easy way. to reduct to 1/4, it takes two half lives, or you do it.