Video: Interpreting Diagrams of Nuclear Reactions

Beryllium-11 is an isotope of beryllium with a half-life of just 13.8 seconds. It can undergo a two-step decay to an isotope of lithium, as shown in the diagram. Red circles represent protons, grey circles represent neutrons, and blue circles represent electrons. What two types of decay does the beryllium nucleus undergo in order to become lithium?

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Video Transcript

Beryllium-11 is an isotope of beryllium with a half-life of just 13.8 seconds. It can undergo a two-step decay to an isotope of lithium, as shown in the diagram. Red circles represent protons. Grey circles represent neutrons. And blue circles represent electrons. What two types of decay does the beryllium nucleus undergo in order to become lithium?

Okay, so, in the diagram given to us, we can see that this is the nucleus that we start with. We’ve been told that this is a beryllium-11 nucleus and undergoes two types of radioactive decay to become lithium. So, let’s start by labeling this nucleus as beryllium. And if we look on the periodic table, we’ll see that beryllium has an atomic symbol Be.

Now, as well as this, we’ve been told that it’s a beryllium-11 atom. And we can recall that this number refers to the mass number of the beryllium atom. So, we can put 11 in the top-left-hand corner, which is traditionally where we write the mass number of an atom. And we can actually verify this with our diagram. Because remember, mass number represents the total number of protons and neutrons in that atom’s nucleus. And in this case, we’ve got one, two, three, four, five, six, seven, eight, nine, 10, 11 nucleons. And so, the mass number is 11.

Additionally, in the bottom-left-hand corner of this atomic symbol, we can put beryllium’s atomic number. Now, this is the total number of protons in the nucleus. And we can do this one of two ways. We could look it up on the periodic table. Or we could count the number of protons given to us in this nucleus in the diagram. Now, since we’ve been told that red circles represent protons, we can count the number of red circles in this nucleus, one, two, three, four. And so, we can put in the atomic number of beryllium, which is four. So, that’s the nucleus that we have at the beginning.

Now, we see that this nucleus then decays into this nucleus plus this blue circle. And of course, blue circles represent electrons. So, we can label that blue circle as an electron, which, we can recall, has an atomic number of negative one and a mass number of zero. This is because the atomic number measures the number of protons in a nucleus, but an electron obviously isn’t made up of any protons.

However, because protons have a relative charge of positive one. We say that an electron has an atomic number of negative one because it’s got the opposite charge to a proton. But the magnitude of that charge is the same. And also, we say that an electron has a mass number of zero because it’s not made up of any protons or neutrons. And so, the total number of protons and neutrons in that electron is zero.

So, we’re saying that this beryllium nucleus then decays into an electron and this nucleus here. Now, currently, we don’t know what this nucleus is, so let’s just call it a generic name. Let’s call it X. And let’s figure out what its atomic and mass numbers are. So, let’s start with the mass number. That’s the total number of protons and neutrons in the nucleus, which happens to be one, two, three, four, five, six, seven, eight, nine, 10 and 11. Hence, we can say that the mass number of this X nucleus is 11. And then, coming to the atomic number, we see that it’s one, two, three, four, five. And we put that value down here.

So, that’s the first radioactive decay of this beryllium nucleus. It goes from a beryllium-11 nucleus to another nucleus with 11 nucleons, but this time five protons rather than four. And as well as this, an electron is emitted. Now, that might be reminiscent of a very particular type of radioactive decay. We can write down this phase of the radioactive decay as a single equation. We can say that the beryllium nucleus is decaying to this unknown nucleus, which we’ve called X, and producing an electron as well.

Now, if we were to check the periodic table for an atom which has five protons, we’d see that this nucleus, which we’ve called X, is actually boron. And boron has a chemical symbol B. So, we’ll replace X with B. But what we can see from this equation that we’ve written down, as well as from the diagram that we’ve been given, is that the total number of protons and neutrons stays the same between the beryllium nucleus and the boron nucleus. However, one of the neutrons in this beryllium nucleus turns into a proton in the boron nucleus.

And so, to simplify the changes. What we see happening is that one of the neutrons in the beryllium nucleus, which we’ll signify with an n, turns into a proton whilst also releasing an electron. Now, this is a very specific type of decay known as beta decay, specifically beta minus decay. And we say that the electron that’s released, so that’s this one here, is known as a beta particle, or a beta minus particle as well.

So, what we figured out is that in the first step, where beryllium turns into boron, the beryllium nucleus has undergone beta decay. And hence, we’ve figured out the first decay process undergone by the beryllium nucleus. So, now, let’s figure out what happens to this boron nucleus when it turns into these two nuclei.

Now, in this case, we can ignore the electron because the electron is not going anywhere or doing anything special. Instead, we only focus on this boron nucleus. The boron nucleus, with five protons and 11 protons plus neutrons, splits into two smaller nuclei, this nucleus and this nucleus. The top one, let’s call Y. And we see that it has one, two, three, four nucleons. So, the mass number is four. And its atomic number is one, two. So, we write down the atomic number here.

And then, looking at the other nucleus, we’ll call this Z. We see that it has a mass number of one, two, three, four, five, six, seven and an atomic number of one, two, three. So, now, we see that our boron nucleus has turned into two nuclei, one of which has an atomic number of two and the other which has an atomic number of three.

Now, we could look up for both of these nuclei on the periodic table. However, we can recall something interesting. We can recall that one of the common types of radioactive decay is alpha decay, where an alpha particle is released. But then, an alpha particle is actually also known as a helium nucleus. And the reason for this is that an alpha particle is actually a nucleus of a helium atom. Where a helium atom is known to have two protons and most commonly two neutrons and, therefore, a mass number of four.

Hence, we could say that our boron nucleus here has undergone alpha decay because it released an alpha particle. And so, we replace Y with either an 𝛼 or the chemical symbol for helium, which is He. And then, all that’s left to do is to work out what Z is. But then, we’ve been told this in the question. We’ve been told that the beryllium atom, which we started with, undergoes a two-step decay to an isotope of lithium. In other words, this other nucleus that’s formed is lithium. So, we can replace Z with the chemical symbol for lithium, which is Li.

And we can confirm this with the periodic table, which will tell us that the element with three protons in its nucleus is indeed lithium. And so, at this point, what we’ve seen is that the beryllium nucleus we started with firstly underwent beta decay to produce a boron nucleus and an electron. And then, the boron nucleus underwent alpha decay to produce a lithium nucleus and a helium nucleus, otherwise known as an alpha particle. So, the two-step radioactive decay was, firstly, beta decay. And then, it was alpha decay. Hence, that is the answer to our question.

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