An isotope can be unstable if its nucleus has either:
Think of the nucleus as a balance scale – if one side (neutrons) is too heavy, the scale tips and the nucleus seeks stability by emitting particles.
| Decay Type | Particle Emitted | Typical Example |
|---|---|---|
| Alpha (α) | \$^4_2\text{He}\$ nucleus | \$^{238}\text{U} \rightarrow ^{234}\text{Th} + \alpha\$ |
| Beta minus (β⁻) | \$e^-\$ (electron) | \$^{14}\text{C} \rightarrow ^{14}\text{N} + \beta^- + \bar{\nu}_e\$ |
| Beta plus (β⁺) | \$e^+\$ (positron) | \$^{22}\text{Na} \rightarrow ^{22}\text{Ne} + \beta^+ + \nu_e\$ |
| Gamma (γ) | High‑energy photon | Often follows any other decay to release excess energy. |
The number of undecayed nuclei after time \$t\$ is given by:
\$N(t) = N0 \left(\frac{1}{2}\right)^{t/T{1/2}}\$
where \$N0\$ is the initial amount and \$T{1/2}\$ is the half‑life.
• When a question asks for the type of radiation, look for clues in the change of atomic number (\$Z\$) and mass number (\$A\$).
• If \$Z\$ decreases by 1 and \$A\$ stays the same, it’s a β⁻ decay.
• If \$Z\$ increases by 1, it’s a β⁺ decay.
• If \$A\$ decreases by 4 and \$Z\$ decreases by 2, it’s an α decay.
• Remember that γ rays do not change \$Z\$ or \$A\$.