Types of Radioactive Decay
Write supplied decay modes with the particles required by charge, nucleon, and lepton bookkeeping.
AP Physics 2 Topic 15.8 · College Board CED printed p. 150, 151 / PDF p. 157, 158 · See this topic in the course outline
Balance a decay by counting what leaves and what changes inside the nucleus. Charge conservation alone is not enough for beta decay.
Before you start
- Nuclear notation
- Nucleon conservation
- Photon energy
Know the particles needed for decay bookkeeping
An AP alpha particle is specifically a helium-4 nucleus, , containing two protons and two neutrons; it is not a neutral helium atom or a helium-3 nucleus. An electron e⁻ has charge −e. A positron e⁺ has the same mass as an electron but charge +e.
Neutrinos ν and antineutrinos ν̄ have no electric charge and negligible mass for these balances. They interact through the weak interaction and gravity and interact very little with ordinary matter. The electron/positron and neutrino/antineutrino are leptons, not nucleons; their A values in nuclear bookkeeping are zero. For lepton-number balances an electron and neutrino contribute +1 each, and a positron and antineutrino −1 each. This sign bookkeeping suffices here; neutrino flavors and detailed distinguishing properties or weak-force mechanisms are outside AP scope.
Balance A, charge, and lepton number
| Mode | Nuclear change | Emitted products | Conservation check |
|---|---|---|---|
| Alpha | A→A−4, Z→Z−2 | ⁴₂He nucleus | daughter + alpha carry original A and charge |
| Beta minus | A unchanged, Z→Z+1 | e⁻ + ν̄ | charge of proton + electron balances neutron; +1−1 lepton number = 0 |
| Beta plus | A unchanged, Z→Z−1 | e⁺ + ν | positron supplies lost positive charge; −1+1 lepton number = 0 |
| Gamma | A and Z unchanged; excitation decreases | photon γ | same nucleus, lower energy, plus emitted photon and recoil |
Beta-minus is inside the nucleus; beta-plus is . Omitting the neutrino partner breaks lepton-number bookkeeping and omits energy/momentum carried away. Electrons emitted in beta decay are created in the nuclear transformation; they are not simply orbital electrons thrown out.
Gamma emission often follows alpha or beta decay when the daughter nucleus is excited. It lowers the energy of that same nucleus: . The photon carries energy and momentum, so the nucleus recoils. Gamma emission does not change the isotope; it can occur from a nuclear excited state without changing nucleon number.
A balanced equation is a constraint, not a complete prediction
Which decay modes are possible depends on the particular isotope and its energy balance; not every formally A- and charge-balanced transformation occurs spontaneously. A problem must provide the mode or enough physical information. Changing isotope can change both the possible decay and half-life, so neither property should be inferred only from element name.
AP Physics 2 does not require memorizing specific isotope pathways or half-lives. The covered modes are alpha, beta-minus, beta-plus, and gamma. Neutron emission as a decay mode and electron capture are excluded; neutron products in a provided fission/fusion reaction are still part of reaction bookkeeping. Neutrino types and detailed weak-force explanations are also excluded.
A beta-minus daughter and its partners
A supplied isotope undergoes beta-minus decay: ¹⁴₆C → daughter + electron + ?. Identify the products and verify A, charge, and lepton number.
A neutron becomes a proton, so A stays 14 and Z rises from 6 to 7; the daughter is ¹⁴₇N.
Why this step? Beta changes nucleon identity without removing a nucleon.
The missing particle is an antineutrino. Charge: 6 = 7 + (−1) + 0. Nucleon count: 14 = 14 + 0 + 0.
Why this step? Include the emitted electron’s charge and zero nucleon count.
Initial lepton number is 0; final electron +1 and antineutrino −1 sum to 0.
Why this step? The neutrino partner completes the conservation accounting.
Answer and check
¹⁴₆C → ¹⁴₇N + e⁻ + ν̄.
Make the model respond
Focused Physics 2 model
Ensemble half-life and nuclear transformations
Predict first. After one half-life, is every nucleus halfway to decaying?
Expected surviving population: N(t) = N₀ 2^(−t/t½); activity = (ln 2/t½)N
- Ensemble expectation
- Selected or reference point
On a narrow screen, scroll within a figure to read its labels. The table and explanation provide the same physics in text.
After 2 half-lives, the expected surviving fraction is 0.25 and N = 1,000. Individual nuclei decay at unpredictable times.
Read the model data and comparisons
| Quantity | Value | Unit | Meaning or limit |
|---|---|---|---|
| Initial number of unstable nuclei | 4,000 | ||
| Illustrative half-life | 5 | s | Adjustable ensemble model; not the physical half-life of the example isotope |
| Elapsed time | 10 | s | |
| Survival probability of one nucleus | 0.25 | ||
| Expected surviving nuclei | 1,000 | Expectation may be fractional; an actual count is an integer | |
| Expected decayed nuclei | 3,000 | ||
| Expected activity | 138.6 | s⁻¹ | |
| Parent (A, Z) | 238, 92 | ||
| Daughter (A, Z) | 234, 90 | ||
| Emitted products | ⁴₂He (alpha) |
The curve predicts an ensemble mean under a constant independent decay probability; it is not a schedule for individual nuclei. In each half-life interval, half of the expected remaining population decays. Actual finite samples fluctuate and have integer counts. A decreases by 4 and Z decreases by 2; the alpha particle is a helium-4 nucleus, not a neutral helium atom. Nuclear mass number counts nucleons, while charge must be conserved including emitted particles. The adjustable seconds-scale half-life is hypothetical, not isotope data for the separate transformation example.
Assumptions and limits. Independent identical unstable nuclei, constant decay probability, one decay stage, no daughter growth/decay chain. N₀ is an initial count and N(t) an expected count. No stochastic simulation or claim that half of every small sample decays exactly in each interval. Transformation examples illustrate A/Z and charge bookkeeping; branching, energy release, and actual isotope half-lives are not modeled.
Try it from memory
Write your answer and reason before opening the worked answer. Your self-assessment is a study decision; it is not an automatically graded score.
Question 1
An alpha emission changes ²¹⁰₈₄Po into what nuclear A and Z? Is the alpha particle electrically neutral?
Worked answer and reason
Daughter A = 206 and Z = 82. The emitted ⁴₂He nucleus has charge +2e; it is not neutral helium.
The specified alpha contains exactly two protons and two neutrons.
Question 2
A daughter nucleus emits a 1.0 MeV gamma photon. Must its element or isotope change?
Worked answer and reason
No. Its A and Z remain unchanged while its nuclear excitation decreases; recoil balances the photon momentum.
Gamma is a lower energy state of the same nucleus, consistent with the fall-2026 definition.
JavaScript enables saved drafts and self-assessment. You can always work on paper.
Catch the tempting mistake
- Beta-minus ejects an electron that was already orbiting the atom.
- The electron is emitted when a neutron changes into a proton, with an antineutrino; nuclear Z increases.
Put it to work
Give the physical reason as well as the calculation. The worked solutions are on a separate page.
- Problem 15 · mixed
- Problem 16 · mixed
- Problem 19 · experimental
Scientific calculator workspace
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Scientific calculator
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For the teacher
- Use electrons and neutrinos with positive lepton number, their antiparticles negative, only for conservation bookkeeping. Do not require neutrino flavors or isotope-pathway memorization.
Source objectives and scope
- 15.8.A — Describe the processes by which individual nuclei decay.
AP Physics 2 does not expect students to memorize the processes by which specific isotopes decay or the half-lives of specific isotopes. Neutron emission and electron capture are not included in the AP Physics 2 curriculum framework. Additionally, types of neutrinos, the characteristics that distinguish neutrinos and antineutrinos, and an explanation or application of the weak force are not within the scope of this course.
Suggested skills are teaching guidance. The course applies all science practices across its objectives.
Science references for this teaching
- AP Physics 2 Course and Exam Description, official Unit 15 — Official topic/LO/EK scope and boundaries; local pinned pages 143–158, equations and relevant clauses visually checked on 143–144,146,149–150,152–158.
- AP Physics 2 Course and Exam Description Clarifications, effective Fall 2026 — 15.7.B.1 current definition includes decay to a lower energy level of the same nucleus.
- OpenStax University Physics 3, Blackbody Radiation — Verification of Wien peak and integrated spectral intensity versus Stefan–Boltzmann total power.
- OpenStax University Physics 3, Photoelectric Effect — Verification of threshold, maximum kinetic energy, intensity distinctions, and retarding-potential experiment.
- OpenStax University Physics 3, The Compton Effect — Verification of positive electron-at-rest shift and photon energy/momentum accounting.
- OpenStax University Physics 3, Nuclear Binding Energy — Verification of all-nucleon mass defect and atomic-mass convention.
- OpenStax University Physics 3, Radioactive Decay — Verification of exponential survival, half-life, and nuclear transformation balances.
- OpenStax University Physics, Volume 3: 6.1 Blackbody Radiation — Primary textbook verification of the wavelength-based blackbody spectral shape, the distinction between peak height and complete spectrum area, Wien’s displacement law, and Stefan–Boltzmann emitted intensity and power.
Glossary and deeper reading · 13 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Photon
A photon is a quantum of electromagnetic radiation with energy proportional to its frequency. It has zero rest mass and no electric charge but carries energy and momentum. For example, increasing light’s frequency increases the energy of each photon, while increasing the number of same-frequency photons increases the total energy.
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Alpha decay
Alpha decay emits a helium-4 nucleus containing two protons and two neutrons. The daughter nucleus has an atomic number smaller by two and a mass number smaller by four. For example, the emitted alpha particle is positively charged because it is a bare nucleus rather than a neutral helium atom.
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Electric charge
Electric charge is a conserved property that determines electric interactions. It can be positive or negative and is measured in coulombs; ordinary net charges arise from an imbalance of charged particles. For example, transferring electrons between initially neutral objects leaves one negatively charged and the other positively charged.
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Neutrino
Neutrinos are electrically neutral elementary particles with very small masses and weak interactions with ordinary matter. Neutrinos and antineutrinos carry energy, momentum, and lepton number in beta-decay accounting. For example, an electron antineutrino accompanies the electron emitted in beta-minus decay.
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Gravity
Gravity is the attractive interaction between masses in the Newtonian model. For spherical bodies or point-mass approximations, its strength decreases with the square of the separation between their centers. For example, Earth’s gravity provides the inward force that keeps a satellite in orbit.
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Beta-minus decay
Beta-minus decay transforms a neutron into a proton while emitting an electron and an electron antineutrino. The nucleus’s atomic number increases by one while its mass number stays fixed. For example, the emitted electron is created in the nuclear transformation rather than being an orbital electron knocked free.
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Beta-plus decay
Beta-plus decay transforms a proton into a neutron while emitting a positron and an electron neutrino. The nucleus’s atomic number decreases by one while its mass number stays fixed, and the reaction must satisfy its energy requirement. For example, the emitted positron has the same mass as an electron but the opposite electric charge.
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Gamma emission
Gamma emission releases a high-energy photon when an excited nucleus moves to a lower nuclear energy state. It changes neither the proton count nor the neutron count, so the isotope can remain the same. For example, a daughter nucleus produced in another decay can subsequently emit a gamma photon as it loses excitation energy.
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Linear momentum
Linear momentum is a vector describing an object’s motion and equals mass times velocity in the nonrelativistic model. The vector sum of momenta is conserved when the net external impulse on the system is zero. For example, two identical carts moving equally fast in opposite directions have zero total linear momentum but nonzero total kinetic energy.
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Isotope
Isotopes are atoms of the same element with different numbers of neutrons. They share an atomic number but have different mass numbers and can differ in nuclear stability. For example, carbon-12 and carbon-14 are isotopes because both have six protons but different neutron counts.
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Half-life
Half-life is the time in which an ensemble of undecayed parent nuclei is expected to decrease to half its initial number. It is a statistical property of the isotope and does not predict the decay time of one nucleus. For example, after two half-lives a large ideal sample has about one quarter of its original parent nuclei remaining.
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Nuclear fission
Nuclear fission splits a nucleus into smaller nuclei and may also emit other particles. The energy outcome depends on the reaction’s mass balance, so not every arbitrary splitting releases energy. For example, fission of an appropriate heavy nucleus can release kinetic energy, photons, and neutrons that can initiate further reactions.
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Nuclear fusion
Nuclear fusion combines smaller nuclei into a larger nucleus and can also emit other particles. Energy release depends on the reaction’s mass balance, and initially the charged nuclei must come close despite electric repulsion. For example, suitable light-hydrogen-isotope reactions can release energy when their products are more tightly bound.