Overview of Balancing Nuclear Reactions

General Chemistry Index

Where are we going with this? This page will assist in developing the ability to compare and contrast nuclear reactions with chemical reactions and to describe nuclear changes in matter, including fission, fusion, transmutations, and decays.

Overview of Balancing Nuclear Reactions

We're going to stick to the big picture… This really isn't that difficult!

But, it IS hard to type, especially in a web page! Therefore, there's going to be a slight adaptation to normal notation methods.

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The hand-drawn image below is "typical" notation. 

Figure 1 is a uranium with 235 mass and 92 protons. (If it had a different number of protons, it wouldn't be uranium. This means it has 235 - 92 neutrons. Which is 143 neutrons.

Figure 2 is plutonium with a mass of 214 and 84 protons.

Hereafter in this article, the symbols will be typed like this: 

²³⁵₉₂U                ²¹⁴₈₄U

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Okay… about balancing nuclear reactions.

Well, the principle is pretty easy, and if we define one more term it gets easier!

A nucleon is a proton or a neutron (since they both normally reside in the nucleus).

You will recall in normal chemical equations, because of the Law of Conservation, the total number of each type of atom from the reactants can be found in the products.

The Law of Conservation is seen, too, in nuclear reactions. However, the inventory is no longer types of atoms, but is nucleons. 

Furthermore, in nuclear reactions, we talk about, not reactants and products (though the concept holds) but rather parent nucleus and daughter nucleus (and yeah… sometimes, "products" will be used, too, when some of the thing produced are not atoms.).

In nuclear reactions, the number of protons in the atoms change. Therefor, the "atom inventory" will not be the same. However…

…in nuclear reactions, the number of nucleons in the parent is the same as those found in the products.

That's it!

So, in balancing nuclear reactions, the masses (top left) and number of protons (bottom left) will always "add up."

Let's say you have three "things" called X, Y, and Z… These could be any kind of atoms or particles.

And let's use a, b, and c for the number of protons and A, B, C for the masses…

So balancing… let's say we do fusion taking an X and Y and making a Z. The balanced equation would fit this form:

^A_aX     +    ^B_bY    →  ^A+B_a+bZ

Now, go back and look again! See how the mass of Z is the sum of the masses of X and Y? See how the proton number of Z is the sum of the proton numbers of X and Y? How 'bout some color?

^A_aX     +    ^B_bY    →  ^A+B_a+bZ

Stop and look again! Seriously! This is really easy!

Okay, so… in a lot of nuclear reactions, there's one thing to start with and it comes apart (decay, fission).

That means the numbers in the products add up to the numbers you started with. If you have a pack of 10 cupcakes that weigh a total of 50 ounces each, and you split it into two bags, each bag will have 5 cupcakes and weight 25 ounces.

When the parent breaks apart it looks like this…

 ^A+B_a+bZ   →   ^A_aX     +    ^B_bY 

Still, not too bad!

You should also keep in mind that there are a few cases where more than one of a certain thing results. As in regular chemical reactions, if more than one of a particular thing is involved, a coefficient will be put in front. It will have the effect of multiplying whatever it proceeds.

So,

2  ⁴₂α 

would mean 4 protons and a mass of 8.

One last thing… Some sources will NOT include the proton number in their equations. You might see this, but you can track that based on the atomic symbols.

For instance…

²²⁶Ra → ²²²Rn + ⁴₂α

Because the atomic symbol is Ra, we know that there are 88 protons. Similarly, because it is Rn, we know that there are 86 protons. Having them included, though, makes the conservation more obvious.

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Okay, some real examples from here:

Alpha decay

The mass and atomic number (proton count) both decrease because an alpha particle has 2 protons and 2 neutrons.

Beta decay

 

A neutron emits a ß particle (massless, "negative proton" / electron) so the mass stays the same but the atomic number (proton count) increases.

Positron Emission

A proton emits a mass-less positron, so the mass stays the same. The proton becomes a neutron, though, reducing the proton count (atomic number) by one

Electron capture

A proton captures an electron, becoming a neutron. Hence, the mass number stays the same, but the atomic number (proton count) decreases. Also, x-ray radiation is produced.

Gamma ray emission

In this example, U-238 decays into "excited" Th-234 which then "relaxes" and gives off gamma rays. Notice that the mass and proton count is equal in all three phases of the reaction because the alpha particle in the middle phase "leaves" the process and never appears in the third phase.

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SUMMARY:

In nuclear reactions:

• The total mass and number of protons will be the same in all stages of the reaction.
  
  
• Changing the number of protons changes the atomic number; the types of elements are NOT the same.
  
  
• If more than one of a particular thing is involved, a coefficient will be put in front. It will have the effect of multiplying whatever it proceeds.