Question Video: Understanding Beta Decay | Nagwa Question Video: Understanding Beta Decay | Nagwa

Question Video: Understanding Beta Decay Physics

When an atomic nucleus emits a beta particle, how much does the atomic number of the remaining nucleus change by?

02:18

Video Transcript

When an atomic nucleus emits a beta particle, how much does the atomic number of the remaining nucleus change by?

Okay, so in this example, we have an atomic nucleus. And this nucleus decays and, in doing so, emits a beta particle, which is an electron. In the process of giving off the electron, the nucleus goes through a change. To see what that change is, let’s represent this emission process using a nuclear equation. We’ll call this element that we start off with element X. And we’ll say that it has an atomic number of 𝑧 and a mass number of 𝐴. We knew that this nucleus emits a beta particle, represented by the Greek letter 𝛽, with an atomic number of negative one and a mass number of zero. In addition to this, there is some leftover nucleus after this emission. We’ll just refer to it using a star symbol. And like any nucleus, this one has a particular atomic number and a mass number.

In this example, we’re specifically wondering how the atomic number of the remaining nucleus ⁠— that’s this one over here ⁠— changes compared to the original nucleus over on the left-hand side. All that to say, we want to figure out what goes here, what is the atomic number of our resulting nucleus, and how that compares to the original atomic number what we’ve called 𝑧. To make this comparison, we can recall that this is a nuclear equation. That means, for one thing, that the total atomic number on the left-hand side is equal to the total atomic number on the right side. In other words, 𝑧, the atomic number of our original nucleus, is equal to negative one, the atomic number of our beta particle, plus whatever goes in the blank, the atomic number of our resulting nucleus.

When it’s written out this way, we can see that the only thing that can go in this blank that makes this equation true is 𝑧 plus one. When we have 𝑧 plus one as the atomic number of our resulting nucleus, then the plus one and the negative one here cancel one another out. And then, we have an equation saying 𝑧 is equal to 𝑧, which is true. So if we start with an atomic number of 𝑧 and then that nucleus goes through beta decay, we wind up with a nucleus with an atomic number of 𝑧 plus one. This means that, in general, when a nucleus emits a beta particle, the atomic number of the remaining nucleus goes up by one. And that’s our answer. The change in the remaining nucleus’s atomic number is plus one.

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