Published by Patrick Mutisya · 14 days ago
Describe the emission of radiation from a nucleus as spontaneous and random in direction.
A nucleus in an excited or unstable state possesses excess energy. Quantum mechanics allows it to lower its energy by
emitting a particle or photon. The probability per unit time that a particular nucleus will decay is constant,
leading to the familiar exponential decay law:
\$N(t)=N_0 e^{-\lambda t}\$
where \$N_0\$ is the initial number of nuclei, \$N(t)\$ the number remaining after time \$t\$, and \$\lambda\$ the decay constant.
Because \$\lambda\$ is a property of the nucleus, the decay cannot be triggered by external factors; it is therefore
spontaneous.
The nucleus is essentially a point source on the scale of the emitted particle’s wavelength. No preferred axis exists,
so each decay has an equal probability of emitting in any solid angle \$4\pi\$ steradians. Over a large number of decays,
the pattern of emitted particles forms a uniform sphere – an isotropic distribution.
| Emission | Particle / Photon | Charge | Mass (u) | Penetrating Power | Typical Energy (MeV) | Effect on Nucleus (A, Z) |
|---|---|---|---|---|---|---|
| Alpha (α) | Helium nucleus (\$^{4}_{2}\alpha\$) | +2 e | 4.0026 | Low – stopped by a sheet of paper | 4–9 | A↓2, Z↓2 |
| Beta (β) | Electron (\$\beta^-\$) or positron (\$\beta^+\$) | –1 e (β⁻) or +1 e (β⁺) | ≈0 (≈9.1 × 10⁻³¹ kg) | Medium – stopped by a few mm of aluminium | 0.01–3 | β⁻: A unchanged, Z↑1; β⁺: A unchanged, Z↓1 |
| Gamma (γ) | High‑energy photon | 0 | 0 | High – requires several cm of lead | 0.1–10 | A unchanged, Z unchanged (often follows α or β decay) |
Alpha decay of uranium‑238:
\$^{238}{92}\text{U} \;\rightarrow\; ^{234}{90}\text{Th} \;+\; ^{4}_{2}\alpha\$
Beta‑minus decay of carbon‑14:
\$^{14}{6}\text{C} \;\rightarrow\; ^{14}{7}\text{N} \;+\; \beta^- \;+\; \bar{\nu}_e\$
Gamma emission following beta decay of cobalt‑60:
\$^{60}{27}\text{Co} \;\rightarrow\; ^{60}{28}\text{Ni} \;+\; \beta^- \;+\; \gamma\$
Nuclear emissions are inherently spontaneous; a nucleus decays because it is energetically favourable, not because of an external trigger.
The emitted particle or photon leaves the nucleus in a random direction, leading to an isotropic distribution of radiation.
Understanding the three main types—α, β, and γ—allows us to predict changes to the nucleus (mass number A and atomic number Z) and to select appropriate shielding.