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

90.2 da

Explanation:

The half-life of iron-59 (45.1 da) is the time it takes for half the Fe to decay.

After one half-life, half (50 %) of the original amount will remain.

After a second half-life, half of that amount (25 %) will remain, and so on.

We can construct a table as follows:

No. of Time Percent Fraction

half-lives days remaining remaining

1 45.1 50 ½

2 90.2 25 ¼

3 135 12.5 ⅛

4 180 6.25 ¹/₁₆

We see that 25 % remains after two half-lives or 90.2 da.