Balancing Nuclear Equations
To balance a nuclear equation, the mass number and atomic numbers of all particles on either side of the arrow must be equal.
Learning Objective

Produce a balanced nuclear equation
Key Points
 A balanced nuclear equation is one where the sum of the mass numbers (the top number in notation) and the sum of the atomic numbers balance on either side of an equation.
 Nuclear equation problems will often be given such that one particle is missing.
 Instead of using the full equations, in many situations a compact notation is used to describe nuclear reactions.
Term

baryon
A heavy subatomic particle created by the binding of quarks by gluons; a hadron containing three quarks. They have halfodd integral spin and are thus fermions.
Full Text
Nuclear reactions may be shown in a form similar to chemical equations, for which invariant mass, which is the mass not considering the mass defect, must balance for each side of the equation. The transformations of particles must follow certain conservation laws, such as conservation of charge and baryon number, which is the total atomic mass number. An example of this notation follows:
To balance the equation above for mass, charge, and mass number, the second nucleus on the right side must have atomic number 2 and mass number 4; it is therefore also helium4. The complete equation therefore reads:
Or, more simply:
Lithium6 plus deuterium gives two helium4s.
The visual representation of the equation we used as an example.
Compact Notation of Radioactive Decay
Instead of using the full equations in the style above, in many situations a compact notation is used to describe nuclear reactions. This style is of the form A(b,c)D, which is equivalent to A + b gives c + D. Common light particles are often abbreviated in this shorthand, typically p for proton, n for neutron, d for deuteron, α representing an alpha particle or helium4, β for beta particle or electron, γ for gamma photon, etc. The reaction in our example above would be written as Li6(d,α)α.
Balancing a Radioactive Decay Equation
In balancing a nuclear equation, it is important to remember that the sum of all the mass numbers and atomic numbers, given on the upper left and lower left side of the element symbol, respectively, must be equal for both sides of the equation. In addition, problems will also often be given as word problems, so it is useful to know the various names of radioactively emitted particles.
Example
This could be written out as uranium235 gives thorium231 plus what? In order to solve, we find the difference between the atomic masses and atomic numbers in the reactant and product. The result is an atomic mass difference of 4 and an atomic number difference of 2. This fits the description of an alpha particle. Thus, we arrive at our answer:
Example
This could also be written out as polonium214, plus two alpha particles, plus two electrons, give what? In order to solve this equation, we simply add the mass numbers, 214 for polonium, plus 8 (two times four) for helium (two alpha particles), plus zero for the electrons, to give a mass number of 222. For the atomic number, we take 84 for polonium, add 4 (two times two) for helium, then subtract two (two times 1) for two electrons lost through beta emission, to give 86; this is the atomic number for radon (Rn). Therefore, the equation should read:
Key Term Reference
 alpha
 Appears in these related concepts: Nucleophilicity & Basicity, Sigmatropic Rearrangements, and Claisen Condensation
 alpha particle
 Appears in these related concepts: The Rutherford Model, The Discovery of the Parts of the Atom, and Nuclear Reactors
 atomic mass
 Appears in these related concepts: The Noble Gases (Group 18), Nuclear Binding Energy and Mass Defect, and Early Ideas about Atoms
 atomic number
 Appears in these related concepts: The Incomplete Octet, Transuranium Elements, and The Periodic Table
 beta particle
 Appears in these related concepts: Modes of Radioactive Decay and Indoor Pollution: Radon
 chemical equation
 Appears in these related concepts: ZeroOrder Reactions, Molecular, Ionic, and Complete Ionic Equations, and MoletoMole Conversions
 decay
 Appears in these related concepts: Radioactive Decay Series: Introduction, Models Using Differential Equations, and Discovery of Radioactivity
 electron
 Appears in these related concepts: Periods 1 through 3, Electrolytic Properties, and Microscopy
 element
 Appears in these related concepts: The Law of Definite Composition, Elements and Compounds, and The Periodic Table
 emission
 Appears in these related concepts: Emission Spectrum of the Hydrogen Atom, New Energy Sources, and The Bohr Model
 mass defect
 mass number
 Appears in these related concepts: Atomic Number and Mass Number, Isotopes, and Average Atomic Mass
 neutron
 Appears in these related concepts: Overview of Atomic Structure, The Bottom of the Periodic Table, and Substances and Mixtures
 nucleus
 Appears in these related concepts: The Shielding Effect and Effective Nuclear Charge, Electric Charge in the Atom, and Clusters of Neuronal Cell Bodies
 photon
 Appears in these related concepts: Fluorescence and Phosphorescence, Energy and Momentum, and Light
 product
 Appears in these related concepts: Measuring Reaction Rates, Writing Chemical Equations, and Basic Operations
 proton
 Appears in these related concepts: Atomic Radius, Development of the Periodic Table, and Cationic ChainGrowth Polymerization
 radioactive decay
 Appears in these related concepts: Alpha Decay, Nuclear Stability, and Tracers
 reactant
 Appears in these related concepts: Physical and Chemical Changes to Matter, The Law of Conservation of Mass, and Chemical Reactions and Molecules
Sources
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