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.

1 Answer
Doc048
Aug 22, 2017

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#

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