Balancing Nuclear Equations

What a Nuclear Notation is

Before diving into nuclear reactions, let's review standard atomic notation, or how elements are shown in the Periodic Table.

In the Periodic Table, each element is represented by a unique chemical symbol. For example, hydrogen has the chemical symbol H, whereas sodium has the chemical symbol Na. The periodic table arranges elements according to their atomic number.

This arrangement of the periodic table based on atomic number can be seen in figure 1. Notice that hydrogen has an atomic number of 1, helium has an atomic number of 2, and so on.

Figure 1. The periodic table of elements

Apart from the chemical symbol and the atomic number, each element also has an average atomic mass.

Now, Nuclear Chemistry uses a special notation to describe nuclear particles. Instead of the atomic mass, they use the term mass number, which is the number of protons plus neutrons (figure 2). The atomic number on the bottom, however, gives the charge on the nuclear particle, but will generally also correspond to the number of protons in an isotope. For example, the nuclear notation of the more radioactive isotope of uranium is \( ^{235}_{92} \text{U} \), meaning that it has 92 protons and 143 neutrons (235 - 92 = 143 neutrons).

Figure 2. Notation in nuclear chemistry

Nuclear Decay and Nuclear Reactions

Nuclear chemistry deals with what happens inside an atom's nucleus, which is where most of its mass is located. But, what's the big deal about nuclear chemistry? During nuclear reactions, mass is actually converted into large amounts of energy!

When dealing with nuclear equations, there are some important nuclear particles featuring unique notations that you need to be familiar with. These are the proton, neutron, alpha, beta, positron, and gamma particle (table 1).

Table 1. Important particles in nuclear chemistry

A neutron particle ( \(^{1}_{0} \text{n} \) ) contains no charge, but it does have a mass number of 1. A proton particle ( \( ^{1}_{1} \text{p} \) ) also has a mass number of 1, but it also has a charge of + 1.

The alpha particle ( \( ^{4}_{2}\alpha \) ) is the equivalent of a helium nucleus (it is not the same thing as a helium atom because an alpha particle does not have any electrons, only protons and neutrons). Alpha particles also have a +2 charge.

Beta particles ( \( ^{0}_{-1}\beta \) ) are also known as electron particles. A β particle has a mass number of 0 and a charge of - 1. A positron particle ( \( ^{0}_{1}\beta \) ), on the other hand, is called an anti-electron particle because it has the same mass number as an electron particle, but with the opposite charge (+ 1). When an electron and a position meet (in other words, when anti-matter meets matter), they "kill" each other, and release lots of energy in the process!

A gamma ray ( \( ^{0}_{0}\gamma \) ) is not a particle and it is refer to as a high-energy photon. It is the electromagnetic energy that is often associated with nuclear radiation (Remember the Electromagnetic Spectrum and the different types of EM radiation that exist!).

When dealing with nuclear chemistry, keep in mind that we are focusing on the nucleus (protons and neutrons), so it is best to "forget" about the electrons and the electron cloud when dealing with nuclear chemistry! Another important term to know is nucleons. Nucleons are found inside the nucleus, and they are bound to each other by a strong nuclear force.

Now, while most nuclei in nature are considered stable, atoms containing a nucleus that is considered radioactive will be unstable and spontaneously emit particles and electromagnetic radiation. This is where nuclear reactions come in! So, let's talk about nuclear decay!

• Any element after Pb (lead) can be considered radioactive!

Nuclear decay (or radioactive decay) can occur through different routes such alpha (\( \alpha \)) decay, beta (\( \beta\)) decay, positron decay or electron capture.

Alpha Decay

Alpha decay, also called alpha emission, tend to happen with heavier elements with an atomic number greater than 82. During alpha decay, the net result is a reduction in mass, emitted an alpha particle ( \( ^{4}_{2}\alpha \) ) as a product. For example, \( ^{210}_{84}\text {Po}\) would undergo alpha decay between it has an atomic number of 84.

$$ ^{210}_{84}\text{Po }\to ^{4}_{2}\alpha\text{ + }^{206}_{82}\text{Po } $$

Beta Decay

Beta decay (or beta emission) occurs when the mass of the isotope is greater than the mass shown in the periodic table. As a result, a beta particle is emitted. For example, in the periodic table, thorium (Th) has a mass of 232.0. So, if we have an isotope of thorium with a mass of 234, it will most likely undergo beta decay.

$$ ^{234}_{90}\text{Th }\to ^{0}_{-1}\beta \text{ + }^{234}_{91}\text{Pa } $$

Electron Capture

Electron capture is basically beta decay in reverse: instead of emitting a β particle, it absorbs a β particle. In order words, the β particle is on the reactant side of the equation. Electron capture can occur when the mass of the isotope is less than the mass shown in the periodic table. For instance, Aluminium-26 would undergo electron capture because its mass is smaller than the mass of Al in the periodic table (26.98).

$$ ^{26}_{13}\text{ Al}+\text{ } ^{0}_{-1}\beta\to \text{ }^{26}_{12}\text{ Mg} $$

Positron Emission

Positron emission also tends to happen in isotopes that have a mass that is less than that on the periodic table. In this type of nuclear decay, a positron particle is given out as a product.

$$ ^{26}_{13}\text{ Al }\to ^{0}_{1}\beta\text{ + }^{26}_{12}\text{ Mg } $$

Rules for Writing Nuclear Equations

When writing nuclear equations, there are some rules we need to follow: always note the type of nuclear decay happening and the nuclear particle involved, and use a periodic table to determine the new nucleus formed after the nuclear reaction.

Let's look at an example.

How to Balance Nuclear Equations

Being able to balance nuclear equations is an essential skill for nuclear chemistry. Let's use an example to better understand this. The nuclear equation below shows a nuclear reaction that occurs in an isotope of uranium. However, notice that there is a particle missing, and it is your job to find out what particle that is in order to balance this equation!

$$ ^{238}_{92}\text{U }\to \text{ }^{234}_{90}\text{Th + ? } $$

Step 1: Balance the mass number on both sides of the reaction.

The first thing we need to do is take a look at the mass number on both sides of the reaction. On the reactant side, we have a mass number of 238, whereas on the product side, we have a mass number of 234. This means that in order to balance this reaction, we need a particle that has a mass number of 4. Why? Because 234 + 4 = 238.

$$ ^{238}_{92}\text{U }\to \text{ }^{234}_{90}\text{Th + } ^{4}_{\square} \text {?} $$

Step 2: Balance the atomic number (charge) on both sides of the reaction.

Now, we do the same thing for the atomic number on the bottom. Since the atomic number change from 92 in the reactant side to 90 on the product side, it means that our nuclear particle needs to have an atomic number of 2.

$$ ^{238}_{92}\text{U }\to \text{ }^{234}_{90}\text{Th + } ^{4}_{2} \text {?} $$

Step 3: Predict the identity of the missing nuclear particle or ray.

Now that you know the mass number and charge of your particle, we can safely predict that the particle needed to balance this nuclear reaction is an alpha particle!

$$ ^{238}_{92}\text{U }\to \text{ }^{234}_{90}\text{Th + } \color{#FA2373} ^{4}_{2} \alpha $$

Balancing Nuclear Equations Practice

The best way to learn the art of balancing nuclear equations is through practice. So, let's solve some problems similar to what you might encounter in your chemistry exam.

Now, I hope that you feel confident in your ability to balance nuclear equations!