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.
