20.2 Nuclear Equations | Chemistry: Atoms First 2e

Learning Objectives

Identify common particles and energies involved in nuclear reactions
Write and balance nuclear equations using mass and charge conservation laws

Core Concepts & Principles

A nuclear reaction alters an atomic nucleus, changing its atomic number ( $Z$ ), mass number ( $A$ ), or energy state. Unlike chemical reactions that conserve total atoms, nuclear reactions rearrange nucleons and obey two strict conservation laws: mass numbers ( $A$ ) and nuclear charges ( $Z$ ) are conserved separately.

Particle Notation & Types

Nuclear equations use specific symbols with mass numbers ( $A$ ) as superscripts and atomic/charge numbers ( $Z$ ) as subscripts:

Proton: ${}_{1}^{1}\text{p}$ or ${}_{1}^{1}\text{H}$
Neutron: ${}_{0}^{1}\text{n}$
Alpha particle: ${}_{2}^{4}\text{He}$ or ${}_{2}^{4}\alpha$
Beta-minus particle: ${}_{-1}^{\,0}\beta$ or ${}_{-1}^{\,0}\text{e}$
Positron: ${}_{+1}^{\,0}\text{e}$ or ${}_{+1}^{\,0}\beta$
Gamma ray: ${}_{0}^{0}\gamma$

Nuclear Charge vs. Ionic Charge

For a nuclide, the left subscript is its proton count $Z$ . For other particles, it is a signed charge number: $-1$ for an electron, $+1$ for a positron, and $0$ for a neutron or photon. A beta particle's mass number is 0 because it is not a nucleon, not because its physical mass is zero. The atom's ionic charge, written as a right superscript, is normally omitted in these nuclear equations.

Core Mental Model: Independent Conservation

Always balance nuclear equations by ensuring the sum of mass numbers and the sum of nuclear charges are identical on both sides.

Problem-Solving Routines & Methods

How to Balance Nuclear Equations and Find Missing Particles

1
Write all known reactant and product nuclides using standard superscript/subscript notation.
2
Sum the mass numbers on the known side and solve for the missing mass number.
3
Sum the nuclear charges on the known side and solve for the missing atomic number.
4
Identify the missing nuclide or particle using its atomic number on the periodic table.

Pro-Tip: Verify that both mass numbers and nuclear charges balance independently before finalizing.

Representative Nuclear Reaction

{}_{12}^{25}\text{Mg} + {}_{2}^{4}\text{He} \longrightarrow {}_{1}^{1}\text{H} + {}_{13}^{28}\text{Al}

Bombardment of magnesium-25 with an alpha particle produces a proton and aluminum-28.

Variables & Constants

A equals mass number;

Z equals atomic number

Practice & Concept Checks

Concept Check

Determine the product of the nuclear reaction where iodine-125 (

{}_{53}^{125}\text{I}

) combines with an electron (

{}_{-1}^{\,0}\text{e}

Concept Check

Why are ionic charges ignored when balancing nuclear equations?

Concept Check

Find the missing particle in the nuclear reaction: ${}_{7}^{14}\text{N} + {}_{2}^{4}\text{He} \longrightarrow {}_{8}^{17}\text{O} + \text{?}

Key Terms & Vocabulary

alpha particleNuclear Particles and Reactions

(α or

{}_{2}^{4}\text{He}

{}_{2}^{4}\text{α})

high-energy helium nucleus; a helium atom that has lost two electrons and contains two protons and two neutrons

beta particleNuclear Particles and Reactions

\text{(β}

{}_{−1}^{\,0}\text{e}

{}_{−1}^{\,0}\text{β}\text{)}

high-energy electron

gamma rayNuclear Particles and Reactions

(γ or

{}_{0}^{0}\text{γ}\text{)}

short wavelength, high-energy electromagnetic radiation that exhibits wave-particle duality

nuclear reactionNuclear Particles and Reactions

change to a nucleus resulting in changes in the atomic number, mass number, or energy state

positron (⁰₊₁β or ⁰₊₁e)Nuclear Particles and Reactions

antiparticle to the electron; it has identical properties to an electron, except for having the opposite (positive) charge

antimatterNuclear Particles and Reactions

particles with the same mass but opposite properties (such as charge) of ordinary particles