Published by Patrick Mutisya · 8 days ago
Radioactive decay is a spontaneous transformation of an unstable atomic nucleus into a more stable configuration. The process occurs randomly; it is impossible to predict when a particular nucleus will decay, only the probability that a large collection of nuclei will decay in a given time.
| Particle | Composition | Charge | Mass (relative to proton) | Typical Change in Nucleus |
|---|---|---|---|---|
| α‑particle | 2 protons + 2 neutrons (\$^{4}_{2}\mathrm{He}\$) | +2e | ≈4 u | \$A \rightarrow A-4,\; Z \rightarrow Z-2\$ |
| β⁻‑particle | Electron (\$e^{-}\$) | –1e | ≈0 u | Neutron → Proton + \$e^{-}\$ + \$\bar{\nu}_e\$ \$A\$ unchanged, \$Z \rightarrow Z+1\$ |
| β⁺‑particle (positron) | Positron (\$e^{+}\$) | +1e | ≈0 u | Proton → Neutron + \$e^{+}\$ + \$\nu_e\$ \$A\$ unchanged, \$Z \rightarrow Z-1\$ |
| γ‑ray | High‑energy photon | Neutral | ≈0 u | Usually follows α or β decay to remove excess energy; \$A\$ and \$Z\$ unchanged |
1. α‑decay of Radium‑226
\$^{226}{88}\mathrm{Ra} \;\rightarrow\; ^{222}{86}\mathrm{Rn} + ^{4}_{2}\alpha\$
2. β⁻‑decay of Carbon‑14
\$^{14}{6}\mathrm{C} \;\rightarrow\; ^{14}{7}\mathrm{N} + e^{-} + \bar{\nu}_e\$
3. β⁺‑decay of Fluorine‑18
\$^{18}{9}\mathrm{F} \;\rightarrow\; ^{18}{8}\mathrm{O} + e^{+} + \nu_e\$
4. γ‑emission after β‑decay (example for \$^{60}\$Co)
\$^{60}{27}\mathrm{Co} \;\rightarrow\; ^{60}{28}\mathrm{Ni}^{*} + e^{-} + \bar{\nu}_e\$
\$^{60}{28}\mathrm{Ni}^{*} \;\rightarrow\; ^{60}{28}\mathrm{Ni} + \gamma\$
The probability that a single nucleus will decay in a short time interval \$dt\$ is proportional to \$dt\$:
\$dN = -\lambda N\,dt\$
where \$N\$ is the number of undecayed nuclei and \$\lambda\$ is the decay constant. Integrating gives the exponential decay law:
\$N = N_0 e^{-\lambda t}\$
The half‑life \$t_{1/2}\$ is the time required for half of the original nuclei to decay:
\$t_{1/2} = \frac{\ln 2}{\lambda}\$