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

Answer 1

For count to reduce to 25%, 2 half-lives would have passed since 1/4 = (1/2)^2. So what do you think is the answer?

Answer 2

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)
t = 65