Question

The element plutonium-239 is highly radioactive. Nuclear reactors

Answer 1

Answer:

$2.84\cdot 10^{-5} y^{-1}$

Step-by-step explanation:

The decay rate of a radioactive isotope (also called activity of the isotope) is given by:

$r=k N$

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

$k=\frac{ln2}{t_{1/2}}$

where

$t_{1/2}$ 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

$t_{1/2}=24,360 y$

Therefore, the k-factor (decay constant) is:

$k=\frac{ln 2}{24,360}=2.84\cdot 10^{-5} y^{-1}$