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 days

Explanation:

All radio decay follows 1st order kinetics and therefore is supported by the integrated rate law of a 1st order decay trend. The classic form of the 1st order decay equation is `A = A_oe^-"kt"` where `A` = final activity (or mass), `A_o` = initial activity (or mass), `k` = the rate constant & `t` = time of decay. The rate constant `(k)` as a function of half-life can be determined from `k*t_(1/2) = 0.693`.

Given `t_(1/2) = 45.1 days` => `k = (0.693/45.1)days^-1` = `0.0154 days^-1`

From the 1st order decay equation ...
`A = A_oe^-"kt"` => `ln(A/A_o) = - k*t`
=> `t = (ln(A/A_o)/-k)` = `(ln(25/100)/-0.0154)days` = `90days`