Here we're told if the decay constant of plutonium 244 is 8.66 * 10 to the -9 years at 25°C, what is its half life? All right, so they're asking for half life and all they're giving us is the decay constant. This is just simply utilizing the radioactive half-life equation.
We're half life equals ln2/K plug in. The value that we just got was 8.66×10^-9 year. Inverse should be inverse. That will give me 8.00×10^7 years.
So this would be our final answer. This would be equal to the half life of plutonium 244. It would take this amount of time for us to lose half of our starting material.