# 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?

###### FREE Expert Solution

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:

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:

96% (106 ratings) ###### 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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