The most abundant isotope of uranium, 238U, does not undergo fission. In a breeder reactor, however, a 238U atom captures a neutron and emits two b particles to make a fis-sionable isotope of plutonium, which can then be used as fuel in a nuclear reactor. Write a balanced nuclear equation.

Video transcript

Hey everyone, we're told that the 2 38 plutonium isotope is one of the abundant isotopes of plutonium, it is not fissile but it can become fissionable if it captures a neutron and emits two beta particles. What is the balanced nuclear equation for the reaction? As we've learned, we can denote our element with the following notation where X represents our element A represents our mass number while Z represents our atomic number. So let's go ahead and write what they've given us. They told us that we had plutonium to 38. Now when we look at our periodic table, we find that plutonium has an atomic number of 94. And we were told that it captures a neutron which we can denote with an end. a mass number of one and an atomic number of zero. Now for our products we have an unknown which we can label as our notation right here with a being our mass number and Z being our atomic number and X as our element. And we were told that it emits two beta particles and we can denote that with our beta and a zero for our mass number and a minus one for our atomic number. So now let's go ahead and balance out our atomic number and our mass number in order to determine our element. Starting with our A. We can see in our react inside we have 2 38 plus one and this is going to be equal to a plus two times zero since we had those two beta particles and our beta particle has a mass number of zero. So when we saw for a we end up with A mass number of 2:39. Now let's go ahead and balance out our atomic number. So we have 94 from our plutonium plus zero from our neutron. And this is going to be equal to Z plus two times negative one, solving for Z. We get 96. Now when we look at our periodic table, we see that the element comes up to be curium. So let's go ahead and write our final balanced nuclear equation. So it's going to be our plutonium 2 38 With an atomic number of 94 plus our neutron. And our product is going to be our curium with a mass number of 239 and an atomic number of 96 plus our two beta particles. And this is going to be our final answer. Now, I hope this made sense. And let us know if you have any questions