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# Balancing Nuclear Equations

At this point in your chemistry journey, you are probably aware of the importance of chemical reactions, and how to balance them. However, when dealing with Nuclear Chemistry, balancing equations can be a bit tricky if you are not familiar with the different nuclear particles that might be involved.

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Table of contents

So, if you want to master the skill of balancing nuclear equations, read on!

• First, we will learn what nuclear notation is.
• Next, we will learn about different nuclear decay reactions.
• After that, we will cover the rules for writing nuclear equations.
• Then, we learn how to balance nuclear equations.
• Lastly, we will work on balancing some nuclear equations to test your understanding.

## 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.

Atomic number is the number of protons that an atom's nucleus contains.

• The number of protons is also equal to the number of electrons the atom has when it is neutrally charged.

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.

The atomic mass of an element is the average mass of all the average occurring Isotopes of that element.

• Isotopes are atoms with the same atomic number but different mass number due to a different amount of neutrons in the nucleus.

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

Check out "Isotopes" to keep learning about them!

## 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).

 Particle/Ray Symbol (${}_{\mathrm{atomic}\mathrm{number}}{}^{\mathrm{mass}\mathrm{number}}\mathrm{X}$) Mass (amu) Charge Proton $$^{1}_{1} \text{p}$$ 1.00728 +1 Neutron $$^{1}_{0} \text{n}$$ 1.00866 0 Beta particle $$^{0}_{-1}\beta$$ or $$^{0}_{-1} \text{e}$$ 0.00015 -1 Positron $$^{0}_{1}\beta$$ 0.00015 +1 Alpha Particle $$^{4}_{2}\alpha$$ 4.00151 +2 Gamma Ray $$^{0}_{0}\gamma$$ 0 0

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!).

These nuclear particles/rays also have penetrating power, and gamma ray is the one with the most penetrating power. This makes sense because if you think about radiation therapy, gamma radiation is so strongly penetrating that it damages even healthy cells!

Alpha particles, on the other hand, have a larger size and a short-range penetrating power, which is why sometimes they are able to kill or damage tumor cells without affecting healthy tissue that is further away from the tumor (neutron-capture therapy).

To put it in a simple way, the smaller the mass of the nuclear particle or ray, the higher its penetration power will be.

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.

Nucleon is the term used to refer to the subatomic particles living in the nucleus (protons and neutrons).

• The mass number can also be referred to as the total number of nucleons in the nucleus!

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 is the spontaneous decomposition of a nucleus that leads to the formation of a different nucleus.

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.

Write the nuclear equation for beta decay of $$^{59}_{26}\text{ Fe}$$.

We learned that beta decay involves the emission of a beta particle as a product. So, we expect that a beta particle will be in the product side of the nuclear equation.

Now, if $$^{59}_{26}\text{ Fe}$$ emits a beta particle ( $$^{0}_{-1}\beta$$ ) as a product, it means that it is losing that beta particle during the reaction. So, after the reaction, the number at the top (mass number) will stay the same because a beta particle has a mass number of 0. However, since the beta particle has an atomic number of -1, it means that the atomic number of the new nuclei will increase by 1.

$$\text {Mass number: 59 - 0 = 0 }$$ $$\text {Atomic number: 26 + 1 = 27}$$

Now that we know that atomic number of the new element (27), look at the periodic table. The element in the periodic table with an atomic number of 27 is cobalt (Co).

Now, we can write the nuclear equation as:

$$^{59}_{26}\text{ Fe}\to ^{0}_{-1}\beta\text{ + }^{59}_{27}\text{ Mg }$$

To check that this is correct, just take a look at the numbers to see if they are the same on each side of the equation. Notice that, on the product side, subtracting 1 from 27 gives an atomic number of 26, which is the same as the atomic number on the reactant side.

## 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.

Balance the nuclear equation below and state the types of nuclear reaction occurring.

$$^{214}_{83}\text{Bi }\text{+ } \text {?} \to \text{ }^{214}_{84}\text{Pb}$$

To balance this equation, we can use the same steps that we just learned. First, look at the mass numbers. Notice that both elements on the reactant and product side have the same mass number (214). Therefore, our missing particle will have a mass number of 0.

Next, we need to balance the atomic numbers. The element on the reactant side has an atomic number of 83, while the element on the product side has an atomic number of 84. This means that we need a nuclear particle with an atomic number/charge of + 1 because 83 + 1 = 84.

The nuclear particle with a mass number of 0 and a charge of +1 is a positron!

$$^{214}_{83}\text{Bi }\text{+ } \color{#FA2373} ^{0}_{+1}\beta \color {blue}\to \text{ }^{214}_{84}\text{Pb}$$

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

## Balancing Nuclear Equations - Key takeaways

• Proton, neutron, alpha, beta, positron, and gamma ray particles are important nuclear particles that might be involved in nuclear decay.
• To successfully balance a nuclear equation, we need to make sure that the mass number and the atomic number is the same on both sides of the equation.
• Balancing nuclear equations can help us predict the type of particle and nuclear decay happening in a nuclear reaction.

## References

1. Theodore Lawrence Brown, Eugene, H., Bursten, B. E., Murphy, C. J., Woodward, P. M., Stoltzfus, M. W., & Lufaso, M. W. (2018). Chemistry : the central science (14th ed.). Pearson.
2. Zumdahl, S. S., Zumdahl, S. A., & Decoste, D. J. (2019). Chemistry. Cengage Learning Asia Pte Ltd.
3. N Saunders, Kat Day, Iain Brand, Claybourne, A., Scott, G., & Smithsonian Books (Publisher. (2020). Supersimple chemistry : the ultimate bite-size study guide. Dk Publishing.

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##### Frequently Asked Questions about Balancing Nuclear Equations

Why do nuclear equations have to be balanced?

As with any other chemical equations, nuclear equations must be balanced due to the law of conservation of mass.

How do you write a balanced nuclear equation for alpha decay?

The result of alpha decay is the reduction of mass and the emission of an alpha particle. The equation below shows an example of a balanced alpha decay nuclear reaction.

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

What is the symbol used for a neutron in balancing nuclear equations?

The symbol used for a neutron in balancing nuclear equation is “n”.

Why is it important to write a balanced nuclear equation?

It is always important to write balanced nuclear equations because of the laws of conservation of mass and charge.

How do you balance a nuclear equation?

To balance a nuclear equation, there are three steps we need to follow:

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

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

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

## Test your knowledge with multiple choice flashcards

The periodic table arranges elements according to their  _______.

The atomic number is the number of _____ that in the nucleus.

The number of protons is also equal to the number of ______ the atom has when it is neutrally charged.

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