The steps below show three of the steps in the radioactive decay chain for ²³²₉₀Th. The half-life of each isotope is shown below the symbol of the isotope. (d) The next step in the decay chain is an alpha emission. What is the next isotope in the chain? [Sections 21.2 and 21.4]

Video transcript

Welcome back everyone. Three of the steps in the radioactive decay chain for plutonium 2 44 are shown in the following diagram below the symbol of each isotope. Are there half lifes identify the next isotope in the chain. If in the next step of the decay chain is an alpha emission. So let's recall that an alpha emission is associated with the objection of our helium isotope, which has a mass number, we recall a four and an atomic number of two. So based on our decay chain, our last steps here is our plutonium 2.40. So this is going to be our reactant. We want to write an equation here where we begin with our reactant plutonium 2 40. It has atomic number 94. And according to our prompt, The next step in our decay chain is an alpha emission and as we stated, an alpha emission results in the release of our isotope helium four. So this is our alpha particle. So what we need to do is just set up an equation to solve for what our next unknown isotope is going to be with its unknown atomic number and unknown or sorry, unknown mass number represented by a an unknown atomic number represented by Z. So all we need to do is set up to equations. So let's give atomic number the color black and we're sorry, mass number. The color black and atomic number. The colors E. So beginning with finding our mass number A. We're going to set up an equation where we understand that We know on our reactant side we have 240, which is set equal to our product side, where we have our unknown atomic number plus are known atomic number. Sorry, our unknown mass number A plus are known mass number of our alpha particle four. So we have a plus four equal to 2 40. And so simplifying this, we would say that A is equal to 236 because we would just take minus four from both sides. So right now we know at least our mask number. And now let's go ahead and move forward to solve for our atomic number Z. Based on what we know from our equation, we can say that our atomic number of 94 is equal to our product side where we have the unknown atomic number Z added to our known atomic number of our alpha particle being too. So we have Z plus two on the product side. And solving for Z, we would subtract two from both sides and say that Z is equal to a value of 92. And so because we now know our atomic number 92, we're going to say that on our periodic table. When we find atomic number 92, we see that this corresponds to the atom uranium. And so plugging in our mass number of 2 36 that we calculated, we have the isotope uranium 2 36 Produced in the next step of our decay chain and this would be our final answer as the next isotope in our decay chain, uranium 2 36. I hope everything I reviewed was clear. If you have any questions, please leave them down below, and I will see everyone in the next practice video.