Beta Decay: Study with Video Lessons, Practice Problems & Examples

Beta decay occurs when an unstable nucleus emits a beta particle, represented as an electron with an atomic mass of 0 and an atomic number of -1. For example, in the decay of mercury-201 (atomic number 80), it transforms into thallium-201 (atomic number 81) while maintaining the same atomic mass. Beta particles are smaller than alpha particles, resulting in lower ionizing power but greater penetrating ability, requiring a sheet of metal or wood for protection against them.

Beta Decay Concept 1

Hey, guys. In this new video, we're going to take a look at beta decay. Now, we're going to say that beta decay occurs when an unstable nucleus somehow emits an electron. Now, we're going to say a beta particle can be represented by E for the electron. Electron here we're going to say is much smaller than the other two subatomic particles, so its atomic mass can just be understood as 0. And here we're going to say its atomic number is negative one because your atomic number is basically the number of protons. Since this is an electron, we're going to say that it's the opposite of a proton which is 1. So, an electron is negative one. Now, we're going to say here beta decay can be represented when we emit a beta particle. For example, if we had mercury-201 (and remember the 201 means that's its atomic mass). So let's say we had mercury-201. If we look on our periodic table, mercury has an atomic number of 80. We're going to emit a beta particle. Now remember, you're going to say your atomic masses have to equal each other on both sides of the arrow and your atomic numbers as well. Here, the electron has no mass, so the new element is going to have a mass of 201. And then here, we have to be very careful. Here this is -one. So -one plus what gives me 80? Well, the answer would have to be 81 because 81 minus 1 gives me the 80 that I had originally. So just remember that. So here would be, Tl. So this would be an example of a beta decay or a beta emission.

Beta Decay Example 1

So, here we have to write the balanced nuclear equations for each of the following beta emissions. Again, beta decay, beta emissions means that the beta particle will be a product. If they had said beta capture or beta absorption, then it would be a reactant. So here we're starting out with magnesium-25. So that's the atomic mass. On our periodic table, magnesium has an atomic number of 12. It's going to emit a beta particle. So, our new element that's being created would still have the same atomic mass. And then here, negative one plus what number gives me 12? It would have to be 13 because 13 minus one gives me the 12 I started out with initially. So, this element would be aluminum. Now, ruthenium-102, we're going to say if we look on our periodic table, ruthenium has an atomic number of 44. Again, we're going to emit a beta particle. So this number stays 102 and this number here would have to be 45. So it goes up to rhodium. Those are the examples of beta decays or beta emissions.

Mg 25 12 → Al 25 13 + β - 1
U 102 44 → Rh 102 45 + β - 1

Beta Decay Example 2

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? So, 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?

So 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 40 calcium, you emit a Helium particle. What do you have now? You're going to have, this is going to be 18, this is going to be 36 and you have argon. 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, 23290. 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 20878 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. Okay. So, 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 emitted 4 of these guys here, which you can just simplify by saying that. So, you can just say 4 times 0 is 0, 4 times negative one is negative 4. 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-1 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 plus 4 Beta decays gives me 20882Pb. 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.

Here’s what students ask on this topic:

What is beta decay and how does it occur?

Beta decay occurs when an unstable nucleus emits a beta particle, which is essentially an electron. This process happens because the nucleus has an excess of neutrons or protons, leading to instability. During beta decay, a neutron in the nucleus is transformed into a proton and an electron. The electron, known as a beta particle, is then emitted from the nucleus. The atomic number of the element increases by one, while the atomic mass remains unchanged. For example, mercury-201 (atomic number 80) decays into thallium-201 (atomic number 81) while maintaining the same atomic mass.

What are the properties of beta particles compared to alpha particles?

Beta particles are smaller than alpha particles, which makes them less damaging in terms of ionizing power. However, their smaller size allows them to penetrate deeper into materials, including human skin. This means that while beta particles have lower ionizing power compared to alpha particles, they have greater penetrating ability. To protect against beta particles, a sheet of metal or a large block of wood is typically required.

How do you balance nuclear equations for beta decay?

To balance nuclear equations for beta decay, you need to ensure that the sum of the atomic masses and the sum of the atomic numbers are equal on both sides of the equation. For example, in the beta decay of mercury-201 (atomic number 80), the equation is:

${\mathrm{Hg}}^{20180}\to {\mathrm{Tl}}^{20181}+e^{0-1}$

Here, the atomic mass remains 201, and the atomic number increases from 80 to 81, balancing the equation.

What materials can stop beta particles?

Beta particles can be stopped by materials that are dense enough to absorb their energy. Common materials used to stop beta particles include sheets of metal, such as aluminum, or large blocks of wood. These materials are effective because they provide enough thickness and density to absorb the beta particles, preventing them from penetrating further.

What is the difference between beta-minus and beta-plus decay?

Beta-minus decay involves the emission of an electron (beta particle) and occurs when a neutron in the nucleus is converted into a proton. In contrast, beta-plus decay involves the emission of a positron (the electron's antiparticle) and occurs when a proton in the nucleus is converted into a neutron. In beta-minus decay, the atomic number of the element increases by one, while in beta-plus decay, the atomic number decreases by one.