Radioactivity

Radioactivity is spontaneous change in an unstable nucleus. It is fundamentally probabilistic: no clock tells when a particular nucleus will decay, yet a large population has a predictable average behaviour characterized by a decay constant and half-life.

Three common emissions change nuclei differently

Alpha decay emits a helium-4 nucleus and lowers A by 4 and Z by 2. Beta-minus decay converts a neutron into a proton while emitting an electron and antineutrino, so A stays fixed and Z rises by 1. Gamma emission releases excess nuclear excitation as a photon without changing A or Z.

Balance A and Z before worrying about names. These changes identify the daughter nuclide.

Activity counts decays per unit time

A = λN

1 becquerel (Bq) = 1 decay per second.

Activity depends on both how many unstable nuclei are present and how rapidly each has a chance to decay. It is not the same as detector count rate, absorbed dose or biological effect.

Statistical does not mean patternless. Ensemble behaviour becomes precise even though individual decay times are random.

Conservation laws constrain each decay

Charge, total energy, momentum and angular momentum must be conserved. Beta decay also involves a neutrino or antineutrino; without it, measured electron energies and momentum balances would not fit conservation laws.

Radiation type and hazard are different questions

Penetration, ionization density, energy, exposure route and biological distribution all matter. Alpha particles are stopped easily outside the body but can deposit energy densely if an alpha-emitting material is internal. Gamma photons penetrate more strongly, but hazard cannot be ranked from particle name alone.

Keep source, radiation and detector separate. A radioactive source has an activity set by its nuclei. The radiation leaving it may be absorbed or scattered before reaching a detector, and the detector records only a fraction of the events that occur. A falling count rate can therefore reflect radioactive decay, changed geometry, extra shielding or detector effects; the physical cause has to be identified before interpreting the number.

Worked examples

1. Alpha daughter

Solution

²³⁸₉₂U undergoing alpha decay gives A=234 and Z=90: thorium-234.

2. Beta-minus daughter

Solution

¹⁴₆C beta-minus decay keeps A=14 and raises Z to 7, giving nitrogen-14.

3. Activity

Solution

If λ=2.0×10⁻5 s⁻1 and N=3.0×10⁸, A=λN=6.0×10³ Bq.