Video: Solving Nuclear Equations Involving Nuclear Fusion

The following nuclear equation shows 2 hydrogen nuclei fusing to form a helium nucleus: _(1)^(1)H + _(1)^(2)H β†’ _(𝑛)^(π‘š)He + energy. What is the value of π‘š in this equation? What is the value of 𝑛 in this equation?

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Video Transcript

The following nuclear equation shows two hydrogen nuclei fusing to form a helium nucleus. What is the value of π‘š in this equation? What is the value of 𝑛 in this equation?

Taking a look at the nuclear equation, we see these two hydrogen nuclei, which are fusing, we’re told, to create helium plus the release of energy. We also see that the atomic numbers as well as the mass numbers of these hydrogen nuclei are shown, whereas the atomic number of helium and its mass number are not shown. It’s those values we want to solve for. And we’ll do it by using the fact that atomic number and mass number is conserved in this reaction. That means that if we add together all the atomic numbers on the left side of the equation, that sum will equal the sum of the atomic numbers on the right side, and same thing with mass number.

Summing the values on the left side will equal the sum of the values on the right. Now on the right-hand side, since our only products are a helium nucleus plus energy, we know that only the helium nucleus will contribute in terms of mass number and atomic number. The energy that’s released in this fusion reaction has no charge and it has no mass. This means that when it comes to answering our first question, what is the value of π‘š, the mass number of helium, we can write that the sum of the mass numbers on the left-hand side of our equation one plus two is equal to π‘š, the mass number of the helium atom. And this tells us that π‘š, the mass number of that atom, is three.

Then moving on to solve for the value of 𝑛, the atomic number of helium, there are a couple of ways we could do this. One is to look up helium on the periodic table of elements and see what element number it is. Another way to solve for 𝑛 is to realize that it must equal the sum of the total atomic numbers on the left-hand side or the reactant side of this equation. So the atomic number of our first hydrogen atom plus the atomic number of our second is equal to 𝑛, the atomic number of helium. And we find that 𝑛 is equal to two, a result we could find using either one of these two methods, either using the periodic table or the fact that atomic number is conserved in this equation.

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