Problem: Iron-59 is a beta emitter with a half-life of 44.5 days. If a sample initially contains 164 mg of iron-59, how much iron-59 is left in the sample after 267 days?

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We’re being asked to determine the mass of iron-59 left after 267 days.


Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:


ln[N]t = -kt + ln[N]0


where:

[N]t = concentration at time t

k = decay constant

t = time

[N]0 = initial concentration


Also, recall that half-life is the time needed for the amount of a reactant to decrease by 50% or one-half


The half-life of a first-order reaction is given by:

t12 = ln 2k


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Problem Details

Iron-59 is a beta emitter with a half-life of 44.5 days. If a sample initially contains 164 mg of iron-59, how much iron-59 is left in the sample after 267 days?

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Our tutors have indicated that to solve this problem you will need to apply the First Order Half Life concept. You can view video lessons to learn First Order Half Life. Or if you need more First Order Half Life practice, you can also practice First Order Half Life practice problems.

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