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.

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.