The decay constant of plutonium-239, a waste product from nuclear reactors, is 2.88 * 10-5 year - 1. What is the half-life of 239Pu?

Video transcript

Welcome back, everyone. We're told that the most stable isotope of radio isotope of thallium thallium 204 has a decay constant of 1.83 times 10 to the negative. First power in verse years determined the half life of thallium 204. We're going to begin by recalling that our decay constant is expressed as the variable K. And we're going to recall that whenever we have radioactive decay, our reaction is under first order kinetics recall that we can utilize the formula for calculating our half life of our radio isotope as the T one half or half life equivalent to the Ln of two divided by our rate constant K. And so in this case, we're going to plug in our given rate constant. So we would have that are half life is equal to in our numerator. The Ln two results in a value of 0.693 and plugging in the denominator our rate constant K given in the prompt as 1.83 times 10 to the negative first power inverse years. So we can go ahead and simplify in our calculators so that we get a half life equal to a value of 3.79 years. And so this would be our final answer highlighted in yellow as the half life of thallium 20204. This will correspond to choice C and the multiple choice. I hope that everything I went through was clear. If you have any questions, please leave them down below and I'll see everyone in the next practice video.