Topic 15.8 Notes – Types of Radioactive Decay

1. What Radioactive Decay Is

An unstable nucleus can rearrange itself into a more stable configuration. When it does, it emits particles or energy. This is radioactive decay.

A quick reminder of nuclear notation:

$$^{A}_{Z}X$$

• Mass number $A$ = protons + neutrons (nucleons)
• Atomic number $Z$ = number of protons
• Element identity depends on Z, not A.

A nuclear reaction looks like:

$$^{A}_{Z}X \rightarrow ^{A'}_{Z'}Y + \text{emitted particles}$$

In every nuclear decay on the AP exam, three things must be conserved:

• Nucleon number (A)
• Electric charge
• Lepton number (electrons, positrons, neutrinos)

If your equation violates one of these, something is missing.

2. Particles Emitted in Radioactive Decay

These are the only particles you need to recognize.

Alpha Particle $\alpha$ or $^{4}_{2}\text{He}$

• 2 protons + 2 neutrons
• Charge = +2
• Mass number = 4
• It’s literally a helium-4 nucleus.

It’s relatively massive and strongly ionizing.

Electron $\beta^{-}$

• Symbol: $^{0}_{-1}e$
• Charge = −1
• Mass number = 0
• Emitted in beta-minus decay

Positron $\beta^{+}$

• Symbol: $^{0}_{+1}e$
• Same mass as electron
• Charge = +1
• Antiparticle of the electron
• Emitted in beta-plus decay

Neutrino $\nu$ and Antineutrino $\bar{\nu}$

• No charge
• Negligible mass
• Interact only through the weak force and gravity → almost never interact with matter
• β⁻ decay emits an antineutrino
• β⁺ decay emits a neutrino

You do not need to distinguish types of neutrinos beyond that.

Gamma Ray $\gamma$

• High-energy photon
• No mass
• No charge
• Pure energy emission

3. The Four Types of Radioactive Decay

Here’s how each one changes the nucleus.

Alpha Decay

$$^{A}_{Z}X \rightarrow ^{A-4}_{Z-2}Y + ^{4}_{2}\alpha$$

The nucleus loses 2 protons and 2 neutrons.

Common in very heavy nuclei (large Z).

Beta-Minus Decay $\beta^{-}$

Inside the nucleus:

$$n \rightarrow p + e^{-} + \bar{\nu}$$

Overall:

$$^{A}_{Z}X \rightarrow ^{A}_{Z+1}Y + ^{0}_{-1}e + \bar{\nu}$$

• A stays the same
• Z increases by 1

This happens when the nucleus has too many neutrons.

Beta-Plus Decay $\beta^{+}$

Inside the nucleus:

$$p \rightarrow n + e^{+} + \nu$$

Overall:

$$^{A}_{Z}X \rightarrow ^{A}_{Z-1}Y + ^{0}_{+1}e + \nu$$

• A stays the same
• Z decreases by 1

This happens when the nucleus has too many protons.

Gamma Decay

$$^{A}_{Z}X^{*} \rightarrow ^{A}_{Z}X + \gamma$$

The asterisk means the nucleus is in an excited state.

No change in A or Z. The nucleus just drops to a lower energy level.

Gamma decay often follows alpha or beta decay.

4. Writing and Checking Nuclear Equations

When you’re given a decay:

1. Identify the decay type.
2. Adjust A and Z correctly.
3. Write emitted particles.
4. Check conservation of A, charge, and lepton number.

Example: Suppose $^{22}_{11}\text{Na}$ undergoes β⁺ decay.

• A stays 22
• Z becomes 10

So:

$$^{22}_{11}\text{Na} \rightarrow ^{22}_{10}\text{Ne} + ^{0}_{+1}e + \nu$$

Quick mental check:

• Mass numbers: 22 = 22
• Charges: 11 = 10 + 1
• Leptons balanced

On multiple-choice, they often hide a missing neutrino or wrong Z change. Always check both A and charge.

5. What Determines the Type of Decay

The isotope itself determines how it decays.

General patterns:

• Too many neutrons → β⁻ decay
• Too many protons → β⁺ decay
• Very large nuclei (Z > 83) → often α decay

You are not expected to memorize specific isotopes or half-lives.

The goal of decay is moving toward a more stable neutron-to-proton ratio.