The fraction of iron-59 after 90 days is 0.25.
Iron-59 decays following first-order kinetics. Given the half-life ([tex]t_{1/2}[/tex]) of 45 days, we can calculate the rate constant (k) using the following expression.
[tex]k = \frac{ln2}{t_{1/2}} =\frac{ln2}{45day} = 0.015 d^{-1}[/tex]
For first-order kinetics, we can find the fraction of Fe ([Fe]/[Fe]₀) after and an elapsed time (t) of 90 days, using the following equation.
[tex]\frac{[Fe]}{[Fe]_0} =e^{-k \times t } = e^{-0.015 d^{-1} \times 90 d } \approx 0,25[/tex]
The fraction of iron-59 after 90 days is 0.25.
You can learn more about kinetics here:
https://brainly.com/question/2284525
