15.8 Types of Radioactive Decay

Radioactive decay is how an unstable nucleus changes into a more stable one by emitting particles or energy. The four types you need to know are alpha, beta minus, beta plus, and gamma decay, and every decay must conserve nucleon number, charge, and lepton number.

Why This Matters for the AP Physics 2 Exam

This topic builds your fluency with writing and balancing nuclear decay equations, a skill that shows up across modern physics questions. You can be asked to identify a daughter nucleus, name the emitted particle, or explain why a given decay conserves charge and nucleon number. These tasks reward careful tracking of mass number and atomic number plus clear reasoning from conservation laws, which is exactly the kind of model-based explanation rewarded in free response.

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Key Takeaways

• Alpha decay ejects a helium-4 nucleus, lowering mass number by 4 and atomic number by 2.
• Beta-minus decay turns a neutron into a proton, emitting an electron and an antineutrino; atomic number goes up by 1, mass number stays the same.
• Beta-plus decay turns a proton into a neutron, emitting a positron and a neutrino; atomic number goes down by 1, mass number stays the same.
• Gamma decay happens after another decay leaves the nucleus in an excited state, releasing a photon with no change to mass or atomic number.
• Every decay conserves nucleon number, electric charge, and lepton number.
• The isotope (its specific mix of protons and neutrons) determines which decay mode occurs.

Particles Involved in Decay

When nuclei decay, they release subatomic particles, each with properties that matter for balancing equations.

• Alpha particles ($\alpha$) are helium-4 nuclei: two protons and two neutrons bound together. They are written as $\alpha$ or $\mathrm{He}^{2+}$ and have a mass of about 4 atomic mass units. In AP Physics 2, only He-4 nuclei are considered.
• Neutrinos ($v$) and antineutrinos ($\bar{v}$) have no electric charge and negligible mass. They interact with matter only through the weak force and gravity, so they pass through normal matter with almost no interaction and are very hard to detect.
• Positrons ($e^{+}$ or $\beta^{+}$) are the antimatter version of electrons: same mass, opposite charge.
• The electrons emitted in beta-minus decay are written $e^-$ or $\beta^-$. They carry charge $-1e$ and have the same mass as ordinary electrons because they are ordinary electrons emitted from the nucleus.

Types of Radioactive Decay

Each decay type involves different particles and changes the nucleus in a specific way.

Alpha Decay

• A nucleus ejects an alpha particle ($\alpha$), reducing its atomic number by 2 and its mass number by 4.
• General equation: $^A_Z X \rightarrow ^{A-4}_{Z-2} Y + ^4_2 \alpha$
• Example: Uranium-238 decays to Thorium-234: $^{238}_{92} \text{U} \rightarrow ^{234}_{90} \text{Th} + ^4_2 \alpha$

Beta-Minus Decay ($\beta^-$)

• A neutron converts to a proton, emitting an electron and an antineutrino.
• Atomic number increases by 1; mass number stays the same.
• General equation: $^A_Z X \rightarrow ^A_{Z+1} Y + e^- + \bar{v}$
• Example: Carbon-14 decays to Nitrogen-14: $^{14}_6 \text{C} \rightarrow ^{14}_7 \text{N} + e^- + \bar{v}$

Beta-Plus Decay ($\beta^+$)

• A proton transforms into a neutron, releasing a positron and a neutrino.
• Atomic number decreases by 1; mass number stays the same.
• General equation: $^A_Z X \rightarrow ^A_{Z-1} Y + e^+ + v$
• Example: Nitrogen-13 decays to Carbon-13: $^{13}_7 \text{N} \rightarrow ^{13}_6 \text{C} + e^+ + v$

Gamma Decay ($\gamma$)

• Gamma decay happens after a nucleus has already undergone alpha or beta decay and is left in an excited state. The excited nucleus drops to a lower energy state by emitting a photon (a gamma ray).
• Neither the atomic number nor the mass number changes.
• General equation: $^A_Z X^* \rightarrow ^A_Z X + \gamma$
• The asterisk marks the excited state of the nucleus.

In all of these processes, three conservation laws must hold:

1. Conservation of nucleon number (total protons plus neutrons)
2. Conservation of lepton number (counting electrons and neutrinos). For example, in beta-minus decay a neutron becomes a proton by emitting an electron and an antineutrino, and in beta-plus decay a proton becomes a neutron by emitting a positron and a neutrino.
3. Conservation of electric charge

Isotope-Specific Decay

The stability of a nucleus depends on its specific mix of protons and neutrons, and that mix sets the decay mode.

• Isotopes with too many neutrons relative to protons tend to undergo beta-minus decay.
• Isotopes with too many protons relative to neutrons often undergo beta-plus decay.
• Very heavy nuclei commonly undergo alpha decay.
• The type of decay a nucleus undergoes is determined by the isotope of the element.

How to Use This on the AP Physics 2 Exam

Problem Solving

Balancing decay equations comes down to two quick checks: the mass numbers (top) on both sides must add to the same total, and the atomic numbers (bottom) must also match. Set up the parent nucleus, subtract the particle that leaves, and read off what is left.

Free Response

If you are asked to explain a decay, name the emitted particle, state how mass number and atomic number change, and tie it back to the conservation laws. A strong answer cites conservation of nucleon number and charge directly rather than just stating the result.

Common Trap

Watch the direction of beta decay. Beta-minus raises the atomic number by 1 (neutron to proton), while beta-plus lowers it by 1 (proton to neutron). Mixing these up flips your daughter nucleus to the wrong element.

Practice Problem 1: Alpha Decay

Solution

Apply conservation of nucleons and charge.

In alpha decay, the parent nucleus emits an alpha particle ($^4_2\text{He}$), which contains 2 protons and 2 neutrons.

Starting with uranium-238 ($^{238}_{92}\text{U}$):

• The mass number decreases by 4: 238 - 4 = 234
• The atomic number decreases by 2: 92 - 2 = 90

The element with atomic number 90 is thorium (Th).

So the daughter nucleus is thorium-234 ($^{234}_{90}\text{Th}$).

The complete nuclear equation is: $^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^{4}_{2}\text{He}$

Practice Problem 2: Beta-Minus Decay

Solution

In beta-minus decay, a neutron converts to a proton, emitting an electron and an antineutrino.

Starting with carbon-14 ($^{14}_{6}\text{C}$):

• The mass number stays the same: 14
• The atomic number increases by 1: 6 + 1 = 7

The element with atomic number 7 is nitrogen (N).

So the daughter nucleus is nitrogen-14 ($^{14}_{7}\text{N}$).

The complete nuclear equation is: $^{14}_{6}\text{C} \rightarrow ^{14}_{7}\text{N} + ^{0}_{-1}e + \bar{v}$

Where $^{0}_{-1}e$ represents the electron (beta particle) and $\bar{v}$ represents the antineutrino.

Common Misconceptions

• Gamma decay does not change the element. A gamma ray carries away energy, not protons or neutrons, so mass number and atomic number stay the same.
• The neutrino and antineutrino are not optional. They are needed in beta decays to conserve lepton number and energy, even though they are nearly impossible to detect.
• An alpha particle is not just any helium. In this course it is specifically a He-4 nucleus with 2 protons and 2 neutrons.
• Beta-minus does not mean a proton leaves. A neutron turns into a proton, and the emitted electron is what carries away the negative charge.
• The emitted electron in beta-minus decay is not one of the atom's orbital electrons. It is created in the nucleus when a neutron becomes a proton.
• More particles emitted does not mean a heavier daughter. Tracking mass number and atomic number, not "how much came out," tells you the resulting nucleus.

Related AP Physics 2 Guides

• 15.1 Quantum Theory and Wave-Particle Duality
• 15.2 The Bohr Model of Atomic Structure
• 15.3 Emission and Absorption Spectra
• 15.6 Compton Scattering
• 15.7 Fission, Fusion, and Nuclear Decay
• 15.4 Blackbody Radiation