Question

Topic: Using exponential and Logarithmic functions
The element plutonium-239 is highly reactive radioactive. Nuclear reactors can produce and also use this element. The heat that plutonium-239 emits has helped to power equipment on the moon. If the half-life of plutonium-239 is 24,360 years what is the value of k for this element? @whpalmer4 Plz I really need help anyone

Answer 1

You can write exponential decay as \[A_0(2)^{-t/t_{1/2}}\]where \(A_0\) is the initial amount at \(t=0\) and \(t_{1/2}\) is the half-life, or time for half of the material to decay into other species.

However, an equally valid and sometimes more useful way of writing it is \[A_0e^{kt}\]where \(k = \large\frac{t_{1/2}}{\ln 2} \approx \frac{t_{1/2}}{0.693}\)