Video: Understanding Beta Decay

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

02:37

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.

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