20.2 Balancing Nuclear Reactions Updated
PRE-HEALTH PREP
Balancing Nuclear Reactions
Mass Numbers, Atomic Numbers & Transmutation Shorthand
General Chemistry 20.2
Lesson Overview
Nuclear reactions are balanced by ensuring that both mass numbers and atomic numbers are equal on each side of the reaction arrow. Common particles in nuclear equations include alpha particles (mass number 4, atomic number 2) and beta particles (mass number 0, atomic number −1), which appear in processes such as alpha decay, beta decay, and electron capture. Nuclear transmutation shorthand provides a compact notation for describing these reactions, using the format Target(bombarding particle, emitted particle)Product.
2 Rules for Balancing Nuclear Reactions
If you have balanced chemical equations and survived the ordeal of balancing redox reactions, here is some welcome news: balancing nuclear reactions is considerably easier. Nuclear equations may be the most straightforward equation balancing you encounter in general chemistry.
In a nuclear reaction, we focus exclusively on the nucleus — protons and neutrons — rather than electrons. We track particles within the nucleus and, occasionally, conversions between protons and neutrons. The fundamental rule for balancing nuclear equations is beautifully simple:
The 2 Rules for Balancing Nuclear Equations
1. Mass numbers must balance on both sides of the reaction arrow.
2. Atomic numbers must balance on both sides of the reaction arrow.
The mass number (A) is the total count of protons plus neutrons. The atomic number (Z) is the number of protons alone. When a nuclear equation contains a mystery particle, determine its identity by finding whatever mass number and atomic number are needed to balance both sides.
Before diving into examples, here is a quick reference for the 4 particles you will encounter most often in nuclear equations:
| Particle | Symbol(s) | Mass Number (A) | Atomic Number (Z) |
|---|---|---|---|
| Alpha particle | 42He or 42α | 4 | 2 |
| Beta particle / Electron | 0−1e or 0−1β | 0 | −1 |
| Proton | 11p or 11H | 1 | 1 |
| Neutron | 10n | 1 | 0 |
Why Mass Numbers and Actual Masses Differ in Nuclear Reactions
Here is an important distinction worth emphasizing: while mass numbers balance perfectly in a nuclear equation, actual masses do not. Every nuclear reaction releases energy, and that energy comes from a small amount of mass being converted according to Einstein's famous equation, E = mc².
If you measured the exact masses of all reactants and products to several decimal places, you would find that the products always weigh slightly less than the reactants. That "missing" mass has been converted into energy — and in nuclear reactions, often a tremendous amount of it.
Mass Numbers vs. Actual Mass: Key Distinction
A mass number is simply the total count of protons and neutrons, rounded to the nearest whole number. For the purpose of balancing nuclear equations, mass numbers balance perfectly. The tiny mass difference that becomes energy only shows up when you use precise, multi-decimal-place masses — not whole-number mass numbers.
So while we balance mass numbers throughout this lesson, keep in mind that a small fraction of mass is always being converted to energy in nuclear reactions. That concept becomes critical when you study nuclear binding energy and nuclear fission later in general chemistry.
Worked Example: Identifying an Alpha Particle (Alpha Decay)
Consider the following nuclear equation in which uranium-238 undergoes alpha decay and produces thorium-234 plus a mystery particle. This is one of the most commonly tested nuclear reactions in general chemistry.
Our job is to identify that mystery particle using the 2 balancing rules for nuclear equations.
Step-by-Step Solution: Balancing Mass Numbers and Atomic Numbers
Balancing mass numbers: The left side has a mass number of 238. Thorium contributes 234 on the right side, so the mystery particle must carry a mass number of 238 − 234 = 4.
Balancing atomic numbers: The left side has an atomic number of 92. Thorium contributes 90, so the mystery particle must have an atomic number of 92 − 90 = 2.
A particle with mass number 4 and atomic number 2 is a helium-4 nucleus, more commonly known as an alpha particle (α).
The complete balanced nuclear equation:
This type of nuclear decay — in which an alpha particle is ejected from the nucleus — is called alpha decay. You can write the alpha particle as 42He or 42α — both notations are acceptable in nuclear equations.
Worked Example: Identifying a Beta Particle (Electron Capture)
In this example, the mystery particle appears on the reactant side rather than the product side. The approach for balancing nuclear equations works exactly the same way — balance both the mass numbers and the atomic numbers.
Step-by-Step Solution: Balancing Mass Numbers and Atomic Numbers
Balancing mass numbers: The product side has a mass number of 214. Bismuth already contributes 214 on the reactant side, so the mystery particle must have a mass number of 214 − 214 = 0.
Balancing atomic numbers: The product side totals 82. Bismuth contributes 83, so the mystery particle must have an atomic number of 82 − 83 = −1.
A particle with mass number 0 and atomic number −1 is a beta particle, also known as an electron.
The complete balanced nuclear equation:
When an electron appears on the reactant side like this, the process is called electron capture — the nucleus literally absorbs an orbiting electron. When an electron instead appears on the product side (ejected from the nucleus during a decay process), it is called beta decay, which is covered in the next lesson.
Electron Capture vs. Beta Decay: Naming Convention
On the reactant side (electron capture), the particle is conventionally written as e for electron. On the product side (beta decay), it is typically written with the β symbol. However, both notations are interchangeable — the particle is the same either way.
How to Read Nuclear Transmutation Shorthand Notation
Nuclear transmutation is the conversion of one nucleus into an entirely different nucleus — the very dream of medieval alchemists who sought to turn base metals into gold. While they never succeeded (lacking both the knowledge and the technology), modern nuclear science can indeed transform one element into another through controlled nuclear reactions.
When scientists describe these nuclear transmutation reactions, they often use a compact shorthand notation that you may be responsible for reading and interpreting on exams.
Reading the Nuclear Transmutation Shorthand Format
Nuclear Transmutation Shorthand Format
Target Nucleus (bombarding particle, emitted particle) Product Nucleus
The comma inside the parentheses represents the reaction arrow. The particle before the comma is a reactant (it collides with the target nucleus), and the particle after the comma is a product (it is emitted alongside the product nucleus).
To translate nuclear transmutation shorthand into a full nuclear equation, place the target nucleus and the bombarding particle on the reactant side, then place the emitted particle and the product nucleus on the product side.
Working Through the Transmutation Example
Consider the following nuclear transmutation written in shorthand, where we need to identify the emitted particle:
First, expand this into a full nuclear equation. The proton (11p) goes on the reactant side with oxygen, and the mystery particle goes on the product side with nitrogen:
Step-by-Step Solution: Balancing the Transmutation Equation
Balancing mass numbers: 16 + 1 = 17 on the reactant side. On the product side, nitrogen contributes 13, so the mystery particle must have a mass number of 17 − 13 = 4.
Balancing atomic numbers: 8 + 1 = 9 on the reactant side. Nitrogen contributes 7, so the mystery particle must have an atomic number of 9 − 7 = 2.
Mass number 4 and atomic number 2 — once again, that is an alpha particle (α).
The complete nuclear transmutation shorthand with the mystery particle identified:
Greek Symbols in Nuclear Transmutation Shorthand
When writing nuclear transmutation shorthand, you must use the Greek symbol for any particle that has one. Write α (not He) and β (not e) inside the parentheses. This is a convention specific to nuclear transmutation shorthand notation.
8 Key Takeaways: Balancing Nuclear Reactions
- In every nuclear reaction, both the mass numbers and atomic numbers must balance on each side of the reaction arrow.
- Nuclear equations deal only with the nucleus (protons and neutrons) — electrons are not part of the balancing process except as beta particles.
- Mass numbers balance perfectly in nuclear equations, but actual masses do not — the small mass difference is converted to energy via E = mc².
- An alpha particle (42α) has mass number 4 and atomic number 2; it is identical to a helium-4 nucleus.
- A beta particle / electron (0−1e) has mass number 0 and atomic number −1.
- Electron capture occurs when a nucleus absorbs an electron from the reactant side; beta decay ejects one on the product side.
- Nuclear transmutation shorthand uses the format: Target(bombarding particle, emitted particle)Product, where the comma represents the reaction arrow.
- In nuclear transmutation shorthand, Greek symbols (α, β) must be used when available — not element symbols like He or e.