Chemistry 2e · Nuclear Chemistry
Nuclear Equations
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In 30 seconds
A nuclear equation describes a change in the nucleus: a parent nuclide The nuclide that undergoes decay. Full entry → transforms into a daughter nuclide The nuclide produced by decay. Full entry → while emitting a particle or photon. Unlike chemical equations, which balance atoms and charge, nuclear equations balance two quantities only: the total mass number A and the total atomic number Z on each side. This topic introduces the notation for particles such as the alpha particle A helium-4 nucleus, 42He. Full entry → 42He, the beta particle A high-speed electron, 0-1e, from neutron-to-proton conversion. Full entry → 0-1e, and the positron An antimatter electron, 0+1e, from proton-to-neutron conversion. Full entry → 0+1e, then shows how to write, complete, and interpret decay equations, including the decay series A chain of decays from a heavy nuclide to a stable end product. Full entry → that carries a heavy nuclide down to a stable end product.
Why this matters
Nuclear equations are the language of nuclear medicine, power generation, and radiation safety. A radiologist reading a technetium-99m scan, a reactor engineer tracking fission products, and a lab worker checking whether an isotope is an alpha or beta emitter all rely on the same balancing rules. For patients and the public, the decay equation reveals the practical questions: what particle leaves the nucleus, how far it travels, and what stable or radioactive element is left behind. Getting the balancing right is also the foundation for calculating half-lives, radiation doses, and the age of archaeological samples.
The college version
Core Concepts
What balances in a nuclear equation
In any nuclear equation, the sum of the mass numbers (top numbers) on the left must equal the sum on the right, and the same holds for atomic numbers (bottom numbers). Charge is conserved automatically because the bottom numbers track the protons. Neutrons and protons convert into each other in beta processes, but the total number of nucleons never changes. These two conservation rules are sufficient to identify an unknown particle or nuclide in a balanced equation.
The common decay particles
The alpha particle is a helium-4 nucleus, 42He, emitted by heavy nuclides; losing it drops A by 4 and Z by 2. The beta particle is a high-speed electron, 0-1e, produced when a neutron becomes a proton; Z rises by 1 and A is unchanged. The positron is an antimatter electron, 0+1e, produced when a proton becomes a neutron; Z falls by 1 and A is unchanged. Gamma rays, 00γ, carry energy only and change neither A nor Z.
Writing a balanced decay equation
To write a decay equation, start from the parent nuclide, add the emitted particle, and solve for the daughter. Choose the parent, for example 23892U emitting an alpha particle. Set up the balance and solve for the daughter's mass and atomic numbers, then identify the element from Z. The same method works for beta decay, positron emission, and electron capture, where a nucleus captures an inner electron, 0-1e, converting a proton into a neutron.
Decay series and chains
A single decay often leaves a still-radioactive daughter, so heavy nuclides travel through a series of steps until they reach a stable end product. Uranium-238, for example, decays through a long chain that includes alpha and beta steps and ends at lead-206. Each step in the chain obeys the same A and Z conservation rules, so you can verify a whole series by checking that every step balances and that A decreases by 4 only on alpha steps.
Common Confusions
| Do Not Confuse | With | Difference |
|---|---|---|
| Beta particle | Electron in an atom | A beta particle is created in the nucleus and emitted; it is not one of the atom's orbital electrons. |
| Positron emission | Beta emission | Positron lowers Z by 1 (proton → neutron); beta raises Z by 1 (neutron → proton). |
| Mass number balance | Chemical equation balancing | Nuclear equations balance A and Z only; atoms, charges, and coefficients as in chemistry do not apply. |
| Alpha decay of a nuclide | Beta decay of the same nuclide | Alpha drops A by 4 and Z by 2; beta changes only Z, by 1. |
| Gamma emission | Any particle emission | Gamma carries no mass or charge, so it changes neither A nor Z. |
| Daughter nuclide | Decay product element | A daughter is the immediate product of one step; series daughters may themselves be radioactive. |
Eli explains
The same idea, in plain words
Explain it like I’m 10
A nuclear equation is a receipt for what happens when a nucleus changes. The top numbers (total pieces) and the bottom numbers (protons) must match on both sides, like making sure both pans of a balance weigh the same. When a heavy nucleus spits out an alpha particle, it loses four pieces and two protons; when a neutron turns into a proton, it sends out a tiny electron called a beta particle.
Worked examples
Write the alpha decay of 23892U. The emitted particle is 42He, so balance the mass numbers:
238 = Adaughter + 4 ⇒ Adaughter = 234
Then balance the atomic numbers:
92 = Zdaughter + 2 ⇒ Zdaughter = 90
The element with Z = 90 is thorium, so the complete equation is:
23892U → 23490Th + 42He
Check: 238 = 234 + 4 and 92 = 90 + 2, so both sides balance. The thorium daughter is itself radioactive and continues the decay series toward lead-206.
Write the beta decay of iodine-131, 13153I, the isotope used in thyroid therapy. A beta particle is 0-1e, so A is unchanged:
131 = Adaughter + 0 ⇒ Adaughter = 131
The atomic numbers balance with the beta particle contributing −1:
53 = Zdaughter + (-1) ⇒ Zdaughter = 54
The element with Z = 54 is xenon, giving:
13153I → 13154Xe + 0-1e
A neutron inside the iodine nucleus became a proton, so the daughter is the next element in the periodic table with the same mass number. This equation is why a patient treated with iodine-131 eliminates xenon-131 as the decay product.
Key takeaways
- Nuclear equations conserve mass number A and atomic number Z; nothing else needs balancing.
- Alpha decay: AZX → A−4Z-2Y + 42He.
- Beta decay: AZX → AZ+1Y + 0-1e; a neutron becomes a proton.
- Positron emission: AZX → AZ-1Y + 0+1e; a proton becomes a neutron.
- Gamma emission changes neither A nor Z; it releases excess energy.
- To find an unknown daughter, subtract the emitted particle's A and Z from the parent's.
- Decay series continue until a stable nuclide forms; alpha steps reduce A by 4, beta steps leave A unchanged.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
What two quantities must balance in every nuclear equation?
Show answer
The total mass number A and the total atomic number Z on each side.
How does alpha decay change the mass number and atomic number of the parent?
Show answer
A decreases by 4 and Z decreases by 2, because a helium-4 nucleus leaves.
In beta decay, what happens inside the nucleus, and how does Z change?
Show answer
A neutron becomes a proton, emitting an electron; Z increases by 1 while A is unchanged.
Write the alpha decay of polonium-210, 21084Po, and identify the daughter.
Show answer
21084Po → 20682Pb + 42He; the daughter is lead-206.
Why does gamma emission not change the identity of a nuclide?
Show answer
Gamma rays carry energy but no mass or charge, so A and Z are unchanged and the nuclide keeps its identity.
What does the beta particle's bottom number of −1 represent?
Show answer
It represents the electron's charge of −1, which is how the atomic-number balance accounts for the emitted electron.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- parent nuclide
- The nuclide that undergoes decay.
- daughter nuclide
- The nuclide produced by decay.
- alpha particle
- A helium-4 nucleus, 42He.
- beta particle
- A high-speed electron, 0-1e, from neutron-to-proton conversion.
- positron
- An antimatter electron, 0+1e, from proton-to-neutron conversion.
- gamma ray
- High-energy photon, 00γ, emitted from an excited nucleus.
- decay series
- A chain of decays from a heavy nuclide to a stable end product.
Sources & references
This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.
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