Now, learning from what we covered with alpha decay and beta decay thus far, we have to try to answer this question. So, here we have lead 208 is formed from thorium 232. How many alpha and beta decays have occurred? Before we even try to answer this question, let's just write down what exactly they're saying. They're saying we created lead 208. So lead-208 is going to be a product. And the atomic number of lead according to our periodic table is 82. And they're saying it was formed from thorium-232. Thorium has an atomic number of 90. Okay, so, what we have to realize next is what exactly does an alpha decay do and what exactly does a beta decay do? Remember, in an alpha decay, we emit a helium particle or an alpha particle. But what does that do exactly to my element? If you go back and look, you should realize that an alpha decay causes a decrease in your atomic mass. So, it decreases atomic mass by 4, and what else does it do? It also decreases your atomic number by 2. So those are the two changes that occur because again we're emitting a helium particle or an alpha particle. So, if you go from calcium-40, you emit a helium particle. What do you have now? You're going to have argon-36. So what happened? The calcium, its atomic mass went from 40 to 36, so it lost 4. Its atomic number went from 20 to 18, so it lost 2. Next, beta decay. What does beta decay do to my element? Well, you emit a beta particle which is 0-1e. So what that does is it increases your atomic number by 1. It doesn't touch the atomic mass at all. And that's the key to this question. If we take a look back at our question now, we go from an atomic mass of 232 to an atomic mass of 208. That is a difference of what? 232-208, that's a difference of 24. Beta decay has nothing to do with my atomic mass at all. It only affects my atomic number by increasing it by 1. So, if I decrease my atomic mass by 4, how many alpha decays is that? So, remember every alpha decay we lose 4, right? So, if we decrease by 24, each alpha decay is 4 lost. So, this represents 6 alpha decays. 6 alpha decays must have occurred for us to lose an atomic mass of 24 overall. So, automatically the answer is going to be either a, b or c. Next, what else happens? We're going to say, okay, if we're losing 6 alpha decays that means we're losing 6 Heliums, right? Now, what we're going to say here, we're going to say 6 times 4 gives me 24 and 6 times 2 gives me 12. So, let's come down here and write down what this is going to be now. So, we're going to say here and guys we're going to need some room to do this. So, let me just take myself out of the image, so we have more room to work with. So, we start out with thorium, 232/90. We know we're going to undergo 6 alpha decays, which is a loss of 24 and a loss of 12 from the atomic number. What does this help to create? Well, this helps to create 208 here and then we're gonna have 78 here. So, if you look on your periodic table, look and see what element has 78. We're going to say that that is platinum. 6 alpha decays helps us create platinum initially. Now, what's the problem? We need now, platinum to go to lead. Remember, what happens with beta decay, we're gonna say with beta decay, your atomic number changes by 1. It increases by 1. So, you need to go from 78 to 82. So, that's an increase of how much? That's an increase of 4 for your atomic number. So, that means you must have had 4 beta decays occur. So c is our answer. So we're going to say 4 beta decays means what? It means that you omitted 4 of these guys here, which you can just simplify by saying that 4×0-1e. Here, I'm just combining everything to make it easier for ourselves. So, you can write it like that or you could have just written it as 4/E-1E. If your professor wanted you to write out the actual reaction, it'd be best to show it like this. But since here I'm just asking you how many beta decays occurred, you can just simply do it like this to make the math easier and faster to do. So, c would be the answer, and if we wanted to show this in the best possible way, we come back and rewrite it as 23290Th and you'd say you have 6 alpha decays + 4 beta decays gives me 208 82 Pb. So, if your professor wants you to show the balanced equation, you have to show it like this. So hopefully, you guys were able to realize that fundamentally what happens with an alpha decay, your atomic mass decreases by 4, your atomic number decreases by 2. And what happens with beta decay? Your atomic number increases by 1. Knowing that alpha decay affects your atomic mass, but beta decay doesn't was the key to answering this question correctly.