Video: Understanding Types of Radioactive Decay

The diagram shows an unstable nucleus undergoing radioactive decay. Red circles represent protons, grey circles represent neutrons, and blue circles represent electrons. What type of radioactive decay does this diagram show?

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Video Transcript

The diagram shows an unstable nucleus undergoing radioactive decay. Red circles represent protons, grey circles represent neutrons, and blue circles represent electrons. What type of radioactive decay does this diagram show?

Okay, so in this diagram, we can see that we’ve got this nucleus here, which we’ve been told is an unstable nucleus. And the reason that we know that this is the unstable nucleus is because these arrows show us that decay products of that nucleus is decayed. In other words then, this nucleus decays into this little circle here and this other nucleus. Now, immediately, we can see that blue circles represent electrons. And so this blue circle is indeed an electron. And then we can go about looking at these two nuclei.

So let’s start with our unstable nucleus. Now, we don’t actually know yet what element this nucleus is. So for now, let’s just call it element X. And let’s start by finding the atomic number and the mass number of this nucleus. So let’s start by doing the mass number first. Now, the mass number of this nucleus is equal to the total number of protons and the neutrons in the nucleus. And we’ve been told that red circles represent protons and grey circles represent neutrons. So we need to count up the total number of red circles and grey circles in this nucleus’ diagram. And that number is equal to one, two, three, four, five, six, seven, eight, nine, 10. Therefore, the mass number of this nucleus is 10. And we write that in the top left-hand corner of our chemical symbol.

So the total number of protons and neutrons in the nucleus is 10. Now to count the number of protons, in order to find the atomic number. And because red circles represent protons, we simply count the red circles, so one, two, three, four. And hence, the atomic number of this unknown nucleus is four. Now, we could go to the periodic table and check which element has four protons in it. But we don’t really need to do that in a second. Instead, what we should do is to now find the same information as we did here for this nucleus. Let’s say now that this nucleus is of element T.

Note that we could have called it something like Y. But actually Y is the chemical symbol for an element. Y is the symbol for yttrium, so we cannot use Y. Similarly, we can’t use W, which is tungsten, or V, which is vanadium, or U, which is uranium. And so we’ll stick with T for now. So this unknown element T firstly has a mass number. That’s the total number of protons and neutrons of one, two, three, four, five, six, seven, eight, nine, 10. Interesting! It’s the same mass number as this element here. In other words, then the total number of protons and neutrons between this nucleus and this nucleus is not changing. However, the atomic number of nucleus T, so that’s the total number of protons, is equal to one, two, three, four, five. And so the atomic number is now five as opposed to four, which is what we had earlier.

And so, based on all of this information, we can actually write a radioactive decay equation. We’ll start with element X, which has four protons and 10 protons plus neutrons. And this decays into element T, which we know has five protons and 10 protons and neutrons, plus an electron. Now, we say that an electron actually has an atomic number of negative one and a mass number of zero. And the reason we say that is the atomic number normally measures the number of protons in the nucleus. And naturally, there are no protons in an electron. However, we say that protons have a relative charge of positive one. And so each time we counter proton in any of these nuclei, we’re basically also calculating the total charge of that nucleus.

And therefore, if each proton adds to the atomic number by positive one, then each electron having the opposite charges of proton should have an atomic number of negative one. It’s negatively charged and has the same magnitude charge as the proton. And then we say that an electron has a mass number of zero because the mass number is the total number of protons and neutrons making up a nucleus. And no protons or neutrons make up an electron in the first place. So the mass number is zero. So now we can look at this equation and try and work out what type of radioactive decay this diagram or this equation is showing. But we can simplify this even further. We can realize that, in going from here to here, the mass number has not changed because both element X and element T have a mass number of 10. And so the total number of protons and neutrons is staying the same.

However, what is changing is the atomic number. We’re going from four to five. In other words, then element T has one extra proton compared to before. But then because the mass number is not changing, there must be one fewer neutrons in T compared to X. In other words, then what we’re saying is that one of the neutrons in element X is being converted into a proton whilst also, of course, releasing the electron, which is here. And we can see that that’s exactly what’s happening in this diagram as well. In the diagram, we’ve got four protons here and six neutrons. So that’s one, two, three, four, five, six. And then one of those neutrons is being converted into a proton.

And from the diagram, it looks like it’s this one, because now we’ve got five protons altogether and only one, two, three, four, five, neutrons. And so a neutron is being converted into a proton and an electron. Now, this type of radioactive decay is known as beta decay or, more specifically, beta minus decay. Because what happens in beta minus decay is that one of the neutrons in an unstable nucleus gets converted into a proton whilst also releasing an electron, otherwise known as a beta minus particle. And so, at this point, we found our final answer. The type of radioactive decay undergone by the unstable nucleus shown in the diagram is beta decay.

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