Nuclear Decay Chain Reference Cheat Sheet

Key Facts

• Isotope notation is written as $_{Z}^{A}\text{X}$, where $A$ is the mass number and $Z$ is the atomic number.
• In alpha decay, a nucleus emits $_{2}^{4}\text{He}$, so the daughter has mass number $A - 4$ and atomic number $Z - 2$.
• In beta minus decay, a neutron changes into a proton and emits $_{-1}^{0}\beta$, so the daughter has mass number $A$ and atomic number $Z + 1$.
• In beta plus decay, a proton changes into a neutron and emits $_{+1}^{0}\beta$, so the daughter has mass number $A$ and atomic number $Z - 1$.
• In gamma emission, a nucleus releases energy as $_{0}^{0}\gamma$, so both $A$ and $Z$ stay the same.
• A balanced nuclear equation has the same total mass numbers and the same total atomic numbers on both sides.
• Half-life is the time required for half of a radioactive sample to decay, and the remaining amount can be modeled by $N = N_0\left(\frac{1}{2}\right)^{t/t_{1/2}}$.
• A decay chain continues through several unstable daughter nuclei until a stable isotope is formed.

Vocabulary

Parent isotope

The unstable starting isotope that undergoes radioactive decay.

Daughter isotope

The isotope produced after a radioactive decay step.

Alpha particle

A helium nucleus written as $_{2}^{4}\text{He}$ that contains $2$ protons and $2$ neutrons.

Beta particle

A high-speed particle emitted during beta decay, written as $_{-1}^{0}\beta$ for beta minus or $_{+1}^{0}\beta$ for beta plus.

Gamma ray

High-energy electromagnetic radiation written as $_{0}^{0}\gamma$ that carries energy but no mass number or atomic number.

Half-life

The time required for the number of undecayed nuclei in a radioactive sample to decrease to one-half of its original value.