Unit 15 · Topic 15.8

15.8 Types of Radioactive Decay

Unstable nuclei decay in four ways you need to know: alpha decay ejects a helium-4 nucleus, beta-minus decay turns a neutron into a proton, beta-plus decay turns a proton into a neutron, and gamma decay releases a photon from an excited nucleus. Every decay conserves nucleon number, charge and lepton number, which is how you balance decay equations. Since fall 2026, the course description says outright that gamma decay counts as radioactive decay, even though the element doesn't change.

Key terms

alpha decay
beta-minus decay
beta-plus decay
gamma decay
positron
neutrino

The particles involved

Alpha particle: a helium-4 nucleus, two protons and two neutrons, written ${}^{4}_{2}\text{He}$ or α.
Electron: ${}^{0}_{-1}\text{e}$ or β⁻. Mass number 0, because it isn't a nucleon.
Positron: the antimatter partner of the electron, same mass but charge +e, written ${}^{0}_{+1}\text{e}$ or β⁺.
Neutrino ν and antineutrino $\bar{\nu}$ : no charge, almost no mass. They interact with matter only through the weak force and gravity, so they pass through almost everything, including the whole Earth.
Gamma ray γ: a high-energy photon, with no mass and no charge.

The four decays

Decay	What happens	Change in A	Change in Z
Alpha (α)	Nucleus ejects ${}^{4}_{2}\text{He}$	Down 4	Down 2
Beta-minus (β⁻)	A neutron becomes a proton; an electron and an antineutrino are emitted	None	Up 1
Beta-plus (β⁺)	A proton becomes a neutron; a positron and a neutrino are emitted	None	Down 1
Gamma (γ)	An excited nucleus drops to a lower energy state, emitting a photon	None	None

Conservation rules

Every decay conserves three things, which lets you fill in a missing piece of any decay equation:

Nucleon number: the top numbers add up the same on both sides.
Charge: the bottom numbers add up the same on both sides.
Lepton number: count electrons and neutrinos as +1 and their antiparticles (positrons and antineutrinos) as −1. The total stays the same. In β⁻ decay, the electron (+1) and antineutrino (−1) add to 0, as before. In β⁺ decay, the positron (−1) and neutrino (+1) also add to 0.

Writing decay equations

Alpha: ${}^{238}_{92}\text{U} \to {}^{234}_{90}\text{Th} + {}^{4}_{2}\text{He}$ . The element changes, because Z changes.

Beta-minus: ${}^{14}_{6}\text{C} \to {}^{14}_{7}\text{N} + {}^{0}_{-1}\text{e} + \bar{\nu}$ . A stays at 14 and Z goes up by 1, so carbon becomes nitrogen.

Beta-plus: ${}^{22}_{11}\text{Na} \to {}^{22}_{10}\text{Ne} + {}^{0}_{+1}\text{e} + \nu$ . Z goes down by 1.

Gamma decay usually follows an alpha or beta decay that leaves the new nucleus in an excited state. Written with a star for \"excited\": ${}^{60}_{28}\text{Ni}^{*} \to {}^{60}_{28}\text{Ni} + \gamma$ . Nothing about A or Z changes.

Which decay a nucleus undergoes depends on which isotope it is. You won't need to memorize which isotopes decay which way, or their half-lives. Neutron emission, electron capture, neutrino types and the details of the weak force aren't part of this course.

Worked examples

Try each one yourself first, then open the solution.

Example 1
Identify the missing nucleus
An unknown nucleus X undergoes beta-plus decay and becomes ${}^{22}_{10}\text{Ne}$ . What is X?
Show the solutionHide the solution
1. Step 1: Write it out: $X \to {}^{22}_{10}\text{Ne} + {}^{0}_{+1}\text{e} + \nu$ .
2. Step 2: Nucleon number: A = 22 + 0 + 0 = 22.
3. Step 3: Charge: Z = 10 + 1 + 0 = 11. Element 11 is sodium.
4. Step 4: So X is ${}^{22}_{11}\text{Na}$ .
Answer: Sodium-22
Example 2
Getting from U-238 to U-234
Uranium-238 ( ${}^{238}_{92}\text{U}$ ) eventually becomes uranium-234 ( ${}^{234}_{92}\text{U}$ ). What combination of alpha and beta-minus decays does this?
Show the solutionHide the solution
1. Step 1: The mass number drops by 4. Only alpha decay changes A, by 4 each time, so there is exactly one alpha decay.
2. Step 2: One alpha decay lowers Z by 2, from 92 to 90. But the final Z is 92 again, so Z must rise by 2.
3. Step 3: Each β⁻ decay raises Z by 1 without changing A, so two β⁻ decays are needed.
4. Step 4: The real sequence: U-238 → (α) Th-234 → (β⁻) Pa-234 → (β⁻) U-234.
Answer: One alpha decay and two beta-minus decays
Example 3
What changes in beta decay? (trap)
Carbon-14 undergoes β⁻ decay. A student writes the product as ${}^{13}_{6}\text{C}$ , reasoning that an electron leaves the nucleus. What's wrong, and what is the correct product?
Show the solutionHide the solution
1. Step 1: An electron has nucleon number 0, so A doesn't change: the product still has A = 14.
2. Step 2: In β⁻ decay a neutron turns into a proton, so Z goes up by 1, from 6 to 7.
3. Step 3: Check charge: 6 = 7 + (−1) ✓. Check lepton number: 0 = (+1 for the electron) + (−1 for the antineutrino) ✓.
4. Step 4: The product is ${}^{14}_{7}\text{N}$ , nitrogen-14.
Answer: The product is nitrogen-14, not carbon-13.

Common mistakes

Thinking beta-minus decay lowers the mass number. The electron has A = 0, so A stays the same and Z goes up by 1.
Mixing up which beta decay emits which neutrino: β⁻ emits an electron and an antineutrino; β⁺ emits a positron and a neutrino.
Changing the element in gamma decay. A gamma ray carries away energy only; A and Z stay the same.
Forgetting that a change in Z means a new element. Look up the symbol that matches the new atomic number.

On the exam

Expect to complete decay equations, identify a decay type from the before-and-after nuclei, or work out a short chain of decays using changes in A and Z.
Justifications should cite the conservation laws by name: nucleon number, charge and, for beta decays, lepton number.

Connected topics

Videos

AP Physics 2 - Unit 15 - Lesson 2 - Radioactive Decay
Allen Tsao The STEM CoachWatch on YouTube (opens in a new tab)
Intro to radioactive decay | Physics | Khan Academy
Khan AcademyWatch on YouTube (opens in a new tab)
Alpha Particles, Beta Particles, Gamma Rays, Positrons, Electrons, Protons, and Neutrons
The Organic Chemistry TutorWatch on YouTube (opens in a new tab)
Beta decay | Physics | Khan Academy
Khan AcademyWatch on YouTube (opens in a new tab)
Conservation of Nucleon Number
Bozeman ScienceWatch on YouTube (opens in a new tab)
Nuclear Chemistry: Crash Course Chemistry #38
CrashCourseWatch on YouTube (opens in a new tab)

Check yourself

4 questions on 15.8 Types of Radioactive Decay. Pick an answer to see if you got it, and why.

Question 1 of 4Calculator allowed

Uranium-238 ( ${}^{238}_{92}\text{U}$ ) undergoes alpha decay. What is the daughter nucleus?

Question 2 of 4Calculator allowed

Carbon-14 undergoes beta-minus decay: ${}^{14}_{6}\text{C} \rightarrow \text{X} + {}^{0}_{-1}\text{e} + \bar{\nu}$ . What is the nucleus X?

Question 3 of 4Calculator allowed

Sodium-22 ( ${}^{22}_{11}\text{Na}$ ) undergoes beta-plus decay. What are the products?

Question 4 of 4Calculator allowed

A nucleus in an excited state undergoes gamma decay. Which statement is correct?

0 of 4 answered