### Video Transcript

The following nuclear equation shows how an isotope of neptunium decays to protactinium. Neptunium, Np, with a mass number of 237 and an atomic number of 93 decays to protactinium, Pa, with a mass number of 𝑚 and an atomic number of 91 plus an 𝛼 particle with a mass number of four and an atomic number of two. What is the value of 𝑚 in the equation?

In order to answer this question, we need to remember the two important rules that we need to follow when constructing a nuclear equation. So what are these two rules? Well, the first rule is that mass number is conserved, and the second rule is that atomic number is conserved. But what does it mean for either of these things to be conserved?

Well let’s take rule number one, mass number, for example. All it means is that on the left-hand side, all of the mass numbers added together has to equal all of the mass numbers added together on the right-hand side. In other words, the total mass number on the left-hand side is exactly the same as the total mass number on the right-hand side.

Since we’re not somehow losing any mass in this equation, the mass number therefore, which actually measures the number of protons and neutrons, must be the same on both sides of the equation. Similarly, rule number two, atomic number is conserved. The total atomic number on the left-hand side is equal to the total atomic number of the right-hand side.

Let’s look at rule number two to begin with just to prove that it does hold for this equation. On the left-hand side, we’ve got 93. So that’s it. We don’t need to worry about anything else. And on the right-hand side, we’ve got 91 plus two. And 93 is in fact equal to 91 plus two. Therefore, rule number two does hold.

Now we look at the rule that we’ll actually use to answer this question, rule number one. On the left-hand side, we’ve got 237 as the mass number. And on the right-hand side, we’ve got 𝑚 and four. Therefore 237 on the left-hand side is equal to 𝑚 plus four on the right-hand side.

And we can rearrange this equation by subtracting four from both sides. That will leave us with just 𝑚 on the right-hand side, and it gives us our final answer, which is that the value of 𝑚 in this equation is 233.