226Ac can decay by any of three different nuclear processes: a emission, b emission, or electron capture. Write a balanced nuclear equation for the decay of 226Ac by each process.

Video transcript

Hey everyone, we're told that the isotope Einsteinian to 52 can have three modes of decay electron capture, alpha decay and beta decay provide the balanced nuclear equation for each mode of decay of Einstein E. Um to 52 1st, let's go ahead and look at electron capture as we've learned, this is when the initial new glide captures an electron so the electron will appear on our react inside. So let's go ahead and figure out our balanced nuclear equation. So we have Einstein E um and it has a mass number of 2 52. And when we look at our periodic table, we find that its atomic number is 99. So for an electron capture, as we said, this will be on our reactant side And its atomic mass is going to be zero And its atomic number is going to be a -1. So now all we have to do is determine our product side and we can do so by balancing out our mass number and our atomic number. So starting off with our mass number, we can see that we have 2 52 from our Einstein E um Plus A zero from our electron. And this will be equal to the mass number of our product. So it looks like our mass number is going to come up to 252. Now let's go ahead and look at our atomic number. Now for our atomic number we have 99 from our Einstein a um and a -1 from our electron. So it looks like our atomic number for our product is going to come up to 98. Now, when we look at our periodic table, it looks like our element is going to come up to be California. So our final balanced nuclear equation will be the element California With an atomic number of 98 and a mass number of 2:52. And this is going to be our final answer for electron capture. Now let's go ahead and look at alpha decay. Now, as we've learned for alpha decay, this will form an alpha particle. So let's go ahead and take the same steps as we did previously. So we have our Einstein E um and we know it has a mass number of 252 and an atomic number of 99. Now for our alpha decay, this will be in our product side. So we have our unknown element And we're going to add in the alpha particle which has a mass number of four And an atomic number of two. Now, let's go ahead and balance out our mass number and our atomic number, Starting with our mass number, we have 252 from Einstein a um and this is going to be equal to the mass number of are unknown Plus four from our alpha particle, solving for our a we're going to get our 2 52 and subtract the four and end up with a mass number of 2 48. Now let's go ahead and look at our atomic number for our atomic number we have 99 from our Einstein E. Um and this is going to be equal to the mass number plus two from our alpha particle. Subtracting two on both sides, We end up with an atomic number of 97. Now when we look at our periodic table, it looks like this will be the element helium. So fixing our equation, it looks like our product is going to be broccoli um With a mass number of 248 And an atomic number of 97. And this will be our final answer for alpha decay. Lastly, let's go ahead and take a look at beta decay. Now for beta decay, we know this forms a beta particle. So the beta particle will appear on our product side. So we have our Einstein e um with a mass number of 252 and an atomic number of 99. This is going to form our unknown element plus our beta particle Which has a mass number of zero and an atomic number of -1. So let's go ahead and balance out our mass number first. So for our mass number, we have 252 from our Einstein a um and this is going to be equal to the mass number of our unknown plus zero from our beta particle. So it looks like our mass number is going to come up to 252. Now let's go ahead and look at our atomic number for our atomic number, we have 99 from our Einstein A. Um and this is going to be equal to the atomic number of our unknown minus one, Adding one on both sides. It looks like our atomic number is going to come up to 100. Looking at our periodic table, our element is going to be for me. Um So updating our equation, our element will be for me um With a mass number of 252 And an atomic number of 100. And these are going to be our final answers now, I hope this made sense and let us know if you have any questions.