### Video Transcript

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

Okay, in this scenario, we have an
atomic nucleus. And this nucleus, we’re told, emits
a beta particle. Now, in general, a beta particle
can be either a beta plus or a beta minus particle. In the problem statement, we’re not
told specifically which type it is. We just know it’s a beta
particle. We do know however that beta minus
radiation is much more common on Earth than beta plus radiation. So if we had to guess, we would say
that this is a beta minus particle. In other words, what’s being
emitted from this nucleus is an electron. Knowing that, we want to figure out
how much the atomic number of the nucleus that remains after the emission of the
electron changes.

One way to answer this question is
to imagine an atomic nucleus of an element, we’ll just call element A. It could be any element. And like any element, it has an
atomic number, we’ll call it 𝑁. And it also has a mass number,
which we’ll call 𝑀. This is the symbol representing the
nucleus that emits a beta particle. In other words, this element goes
through a radioactive transformation. It emits a beta particle, an
electron, which has a mass number of zero because there are no protons or neutrons
in it. And it has an atomic number of
negative one because the charge of this beta particle is equal and opposite the
charge of a proton. And then, of course, along with the
emitted electron, there’s the nucleus that’s left over. We’ll say it’s a nucleus of an
element B.

In an equation like this, and in
general in nuclear equations, both mass number as well as charge is conserved. So that means the mass number on
the left-hand side of the equation, in this case 𝑀, is equal to the sum of the mass
numbers on the right-hand side. That tells us that the mass number
for element B must be 𝑀 in order for that equality to hold true. But then, what about atomic number,
the number written to the lower left of these symbols.

Knowing that atomic number is also
conserved, we can say that 𝑁 is equal to negative one, the atomic number of the
beta particle, plus the atomic number of our element B. In order for this equality to be
true, we can say what goes in the parentheses. It has to be 𝑁 plus one. That way, the plus one cancels with
the minus one. And we just have 𝑁 is equal to
𝑁. So the atomic number of our product
nucleus is 𝑁 plus one.

That’s not our final answer though
because the question asks how much does the atomic number of the remaining nucleus
change. In other words, when we go from
element A to element B, how much of a change in atomic number is there. Since the atomic number of A is 𝑁
and the atomic number of B is 𝑁 plus one, we can see that the overall change is
plus one. That’s the change in the atomic
number of the remaining nucleus.