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# Writing nuclear equations for alpha, beta, and gamma decay

## Video transcript

- [Voiceover] Let's look at three types of radioactive decay, and we'll start with alpha decay. In alpha decay, an alpha particle is ejected from an unstable nucleus, so here's our unstable nucleus, uranium-238. An alpha particle has the same composition as a helium nucleus. We saw the helium nucleus in the previous video. There are two protons in the helium nucleus and two neutrons. So I go ahead and draw in my two neutrons here. Since there are two protons, the charge of an alpha particle is two plus. So for representing an alpha particle in our nuclear equation, since an alpha particle has the same composition as a helium nucleus, we put an He in here, and it has two positive charges, so we put a two down here, and then a total of four nucleons, so we put a four here. Trying to figure out the other product from our nuclear equation, I know nucleons are conserved, so if I have 238 nucleons on the left, I need 238 nucleons on the right. Well, I have four from my alpha particle, so I need 234 more. So 234 plus four gives me a total of 238 on the right, and so therefore nucleons are conserved here. In terms of charge, I know charge is also conserved. On the left, I know I have 92 protons, so 92 positive charges on the left. I need 92 positive charges on the right. We already have two positive charges from our alpha particle, and so we need 90 more. So we need 90 positive charges. We need an atomic number here of 90. The identity of the other product, just look it up here at our table, find atomic number of 90, and you'll see that's thorium here. So thorium-234 is our other product. So we think about what's happening visually, we're starting off with a uranium nucleus which is unstable, it's going to eject an alpha particle, so an alpha particle is ejected from this nucleus, so we're losing this alpha particle, and what's left behind is this thorium nucleus. So this is just a visual representation of what's going on here, in our nuclear equation. Let's do beta decay. So in beta decay, an electron is ejected from the nucleus. We saw in the previous video that you represent an electron, since it has a negative one charge, you put a negative one down here, it's not a proton, nor is it a neutron, so we put a zero here. So here's our electron and an electron ejected from the nucleus is called a beta particle. We could put a beta here, and it's an electron, so a negative one charge, and then a zero here. If a beta particle is ejected from the nucleus of a thorium-234, so we're starting with thorium-234, this nucleus ejects a beta particle, so we go ahead and put a beta particle in here, so zero and negative one, what else is produced here? What else do we make? Well, once again, the number of nucleons is conserved, so I have 234 nucleons on the left, I need 234 on the right. I have a zero here, so I need 234 nucleons. Charge is also conserved, so I have 90 positive charges on the left, I have 90 protons. On the right, I have a negative charge here, so I have a negative one charge, and so I must need 91 positive charges, because 91 positive charges and one negative charge gives me 90 positive charges on the right. So I need an atomic number of 91. If you look at the periodic table, and you find the atomic number of 91, you'll see that this is protactinium. So we're going to make protactinium here, so Pa. What is happening in beta decay? Let's look at it in a little bit more detail. We already talked about the number of protons, so we have 90 protons on the left, how many neutrons do we have? Well, 234 minus 90, 234 minus 90 gives us the number of neutrons. That's 144 neutrons. On the right, we have 91 protons, how many neutrons do we have? Well, that'd be 234 minus 91. So 234 minus 91 gives us 143 neutrons. So we went from 144 neutrons on the left to 143 neutrons on the right, and we went from 90 protons on the left, to 91 protons on the right. So we lost a neutron, and we gained a proton. You could think about the neutron turning into a proton, and this is an oversimplified way of thinking about it. Let's go ahead and write that down here. So a neutron turning into a proton. So a neutron has no charge, so we put a zero here. And a neutron is a nucleon, so we put a one right here. So a neutron is turning into a proton, so let's go ahead and write our proton here. A proton has a plus one charge, and it's a nucleon so we put a one here. When we think about what else is made, we know that nucleons are conserved, so we have one nucleon on the left, one nucleon on the right. Therefore, we would have a zero here. In terms of charge, if we have zero charge on the left, plus one on the right, we need negative one right here. This of course represents the electron, so this is the electron that's ejected from the nucleus. This is our beta particle. And also actually, something else is produced. You're also going to make an anti-neutrino, and that's just really not part of this video, so we'll just ignore it for now. So a neutron has turned into a proton, and we're also getting a beta particle ejected from the nucleus. When this conversion, this process is actually governed by the weak force, the weak interaction, so there's a lot of stuff going on in the nucleus which we just won't get into in this video. The important thing is to be able to look at a nuclear equation, recognize it as beta decay, and be able to write everything in your nuclear equation. Let's do one more type of decay. This is gamma decay. Gamma rays are given off, and a gamma ray has no charge and no mass; it's pretty much just energy, if you think about it. These are pretty easy decay problems. Let's start with technetium-99m, and the m right here stands for metastable, which means a nucleus in its excited state, so a nucleus in its excited state, so it has more energy. It's going to give off a gamma ray, so let's go ahead and draw in our gamma ray here, so zero and zero. Since we're dealing with zeroes, so these zeroes aren't going to affect our numbers, so if we start with nucleons, we have 99 nucleons on the left, we're going to have 99 nucleons on the right. And in terms of charges, we have 43 positive charges on the left, we need 43 positive charges on the right. And since the atomic number isn't changing, it's 43 on the left, it's 43 on the right, we're dealing with technetium here. It's still technetium; it's just in the ground stage. It's no longer in the excited state. It's in the ground state. It's given off energy in the form of gamma rays in this example here. So technetium-99m is actually used in several medical imaging and diagnostic procedures, because we have ways of measuring the gamma radiation, and so this is very useful in medicine.