What you'll be able to do: Identify alpha, beta, positron and gamma decay and balance any nuclear equation by conserving mass number and charge.
Nuclear reactions change the nucleus itself, not just the electrons around it. Once you know what each decay particle does to the mass number and the atomic number, every nuclear equation becomes a two-line bookkeeping problem.
These are recommended, not required. You can start this lesson at any time.
A nuclide is written with its mass number (protons + neutrons) on the upper left and its atomic number (protons) on the lower left of the element symbol. In plain text this lesson writes it as element-massnumber, for example ²³⁸U.
The atomic number is fixed by the element symbol, so it is the mass number that tells you which isotope you are dealing with.
²³⁸₉₂U has 92 protons and 146 neutrons.
The upper-left number A counts nucleons, not the particle's mass in atomic mass units. A beta electron has A = 0 because it contains no protons or neutrons, but it has nonzero rest mass. The lower-left number is charge in elementary-charge units for the emitted particle. For a nuclide that number is Z, the proton count.
| Particle | Nuclear equation symbol | A | Charge / e |
|---|---|---|---|
| Alpha, helium nucleus | ⁴₂He | 4 | +2 |
| Beta minus, electron | ⁰₋₁e | 0 | −1 |
| Positron | ⁰₊₁e | 0 | +1 |
| Neutron | ¹₀n | 1 | 0 |
| Gamma photon | ⁰₀γ | 0 | 0 |
A photon has zero rest mass but carries energy and momentum. An alpha particle is a helium nucleus, not initially a neutral helium atom with two bound electrons.
Alpha decay: mass number falls by 4, atomic number falls by 2. Beta-minus (β⁻) decay: mass number unchanged, atomic number rises by 1. Positron emission or electron capture: mass number unchanged, atomic number falls by 1. Gamma emission: neither number changes, only energy is released. Learning these four rows is most of the topic.
In β⁻ decay, n → p + e⁻ + antineutrino: A stays fixed, Z rises by one and neutron count falls by one. In β⁺ decay, p → n + e⁺ + neutrino: Z falls by one. Electron capture uses p + e⁻ → n + neutrino and also lowers Z by one. Neutrinos have zero A and charge, so introductory A/Z balancing often omits them, but a complete energy, momentum and lepton account includes them. Beta electrons are created in the decay process; they are not pre-existing electrons stored as ordinary nuclear constituents.
Add the mass numbers on each side and set them equal; do the same with the atomic numbers. For the specified single missing particle or daughter, the A and charge-number balances identify its nuclear symbol; a complete process may additionally include neutral particles such as neutrinos. Once you have its atomic number, the periodic table gives you the element symbol.
For an unknown daughter in ²³⁸₉₂U → daughter + ⁴₂He, solve Adaughter = 238 − 4 = 234 and Zdaughter = 92 − 2 = 90, then identify thorium. For electron capture, include the captured electron on the left: ⁷₄Be + ⁰₋₁e → ⁷₃Li + neutrino. The charge-number sum is 4 − 1 = 3. Gamma emission from an excited ⁹⁹ᵐTc nucleus gives ⁹⁹Tc without changing the element or isotope's mass number; only its excitation state changes.
sum of mass numbers (left) = sum of mass numbers (right); sum of atomic numbers (left) = sum of atomic numbers (right)
Light stable nuclei often have N/Z near one, while heavier stable nuclei require more neutrons to offset proton repulsion. A neutron-rich isotope often undergoes β⁻ decay; a proton-rich isotope may undergo β⁺ emission or electron capture. Many very heavy nuclei undergo alpha decay, but beta decay and spontaneous fission can also compete. Neither high mass nor N/Z alone uniquely determines a decay route or its half-life.
The proposed decay must release energy and obey the relevant conservation rules. With neutral atomic masses, positron emission needs a parent–daughter mass excess exceeding two electron masses, about 1.022 MeV/c²; electron capture can be allowed when positron emission is not. Use the specified mode or evaluated decay data when a unique daughter is requested. A balanced nuclear equation demonstrates bookkeeping consistency, not energetic permission.
In positron emission, a proton becomes a neutron while emitting a positron; in electron capture, a proton captures an inner electron to become a neutron. Both reduce atomic number by one while leaving mass number unchanged.
They differ in the particle appearing on the reactant or product side; a neutrino is also involved in a complete particle account.
A helium-4 nucleus: mass number 4, charge +2.
An electron emitted when a neutron becomes a proton: mass number 0, charge -1.
A particle with the electron's mass and the opposite charge: mass number 0, charge +1.
Nucleon number and electric charge balance in the modes taught here; total mass-energy, momentum and other particle conservation laws also apply.
Too many neutrons favours beta-minus (β⁻); too few favours positron emission or electron capture; too heavy favours alpha.
X(A, Z) → Y(A − 4, Z − 2) + ⁴₂He
X(A, Z) → Y(A, Z + 1) + ⁰₋₁e + electron antineutrino
X(A, Z) → Y(A, Z − 1) + ⁰₊₁e + electron neutrino
Uranium-238 undergoes alpha decay. Write the balanced nuclear equation and name the daughter nuclide.
Try it first: Before reading on, subtract the alpha particle's mass number and atomic number from uranium's and see which element you land on.
0 of 4 steps revealed.
carbon-14 decays by beta-minus (β⁻) emission. Write the balanced equation.
0 of 4 steps revealed.
Fill in the missing particle: ⁷₄Be + ⁰₋₁e → ? (electron capture)
0 of 3 steps revealed.
Sodium-22 undergoes positron emission. Identify the daughter nuclide and compare its A and Z with electron capture.
Try it first: Na has Z=11, and a positron has A=0, Z=+1.
0 of 3 steps revealed.
| Mistake | Why it's wrong | Check instead |
|---|---|---|
| Giving a beta particle a mass number of 1 because a neutron changed into a proton. | The nucleon count does not change in beta decay, only the identity of one nucleon; the emitted electron has mass number 0. | Always write the beta particle as mass 0, charge -1, then confirm the mass numbers already balance. |
| Moving the element the wrong way on the periodic table after beta decay. | Beta-minus (β⁻) raises the atomic number, so the daughter is one place to the right, not the left. | Work out the daughter's atomic number numerically first, then look up that number on the table. |
| Assuming gamma emission produces a new element. | A gamma ray has zero rest mass, mass number and electric charge, while carrying energy and momentum, so both numbers are unchanged. | Treat gamma emission as the nucleus dropping to a lower energy state, nothing more. |
Scroll horizontally if needed to read all columns.
After the lesson · Question bank
Work through new problems on your own. The lesson's quick checks and worked examples stay above if you need to review a step.
19 topic questions across 3 difficulty levels.
Loading practice questions…
Radioactive nuclei become more stable by emitting particles or energy. Alpha decay ejects a helium-4 nucleus, lowering the mass number by 4 and the atomic number by 2. Beta-minus (β⁻) decay converts a neutron into a proton and ejects an electron, raising the atomic number by 1 at constant mass number. Positron emission and electron capture do the opposite, lowering the atomic number by 1. Gamma emission releases energy only and changes neither number. Every nuclear equation must balance twice: the sum of mass numbers on the left equals the sum on the right, and the same is true of the atomic numbers.
Lesson: Not marked completed
Marking a lesson completed records that you finished reading it. Practice establishes mastery separately. Saved on this device.
Try a short set of different questions to check what you can do independently.
An optional video to support this lesson.
Loading video resources…
External resources belong to their respective creators. Chem Help is not affiliated with or endorsed by these providers. Links open the original provider; their terms apply.
Source attribution for this lesson has not been verified. Missing source records do not establish originality or reuse permission.