Answer:
[tex]2.84\cdot 10^{-5} y^{-1}[/tex]
Step-by-step explanation:
The decay rate of a radioactive isotope (also called activity of the isotope) is given by:
[tex]r=k N[/tex]
where
r is the decay rate
k is the decay constant
N is the number of nuclei in the radioactive sample
The decay constant of a radioactive isotope is also related to the half-life of the isotope by the formula
[tex]k=\frac{ln2}{t_{1/2}}[/tex]
where
[tex]t_{1/2}[/tex] is the half-life of the isotope, which is the time taken for the sample to halve, compared to its initial amount
In this problem, the half-life of plutioniun-239 is
[tex]t_{1/2}=24,360 y[/tex]
Therefore, the k-factor (decay constant) is:
[tex]k=\frac{ln 2}{24,360}=2.84\cdot 10^{-5} y^{-1}[/tex]
