Modes of Radioactive Decay

Introduction to Radioactive Decay

Nucleons (protons and neutrons) are held together in the nucleus by the strong nuclear force, which is much stronger than the proton-proton Coulomb repulsive force but acts only over very short ranges (a few femtometers). To achieve a stable nucleus, the number of protons (Z) and neutrons (N) must be balanced. In lighter elements, the number of protons and neutrons is approximately equal (Z = N), but for heavier nuclei (A > 40), more neutrons than protons are required to counteract the Coulomb repulsion between protons.

If the number of protons and neutrons is not in an optimal balance, the nucleus becomes unstable (radioactive) and undergoes decay to a more stable configuration. This process continues through various intermediate unstable states until a stable nuclide is formed. Radioactive decay is classified into several modes based on the type of radiation emitted and the nature of the transformation.

Main Categories of Radioactive Decay

Radioactive decay can occur through one of six main types, three of which are most important for medical applications:

Alpha (α) Decay
Beta (β) Decay (including β– decay, β+ decay, and electron capture)
Gamma (γ) Decay (including pure γ decay and internal conversion)

There are also less commonly observed modes of decay, including:

Spontaneous Fission
Proton Emission
Neutron Emission

Alpha (α) Decay

Alpha decay is a common mode of decay for heavy nuclei. In this process, the nucleus emits an alpha particle (helium nucleus: ⁴He) consisting of two protons and two neutrons. This process reduces the atomic number (Z) by 2 and the mass number (A) by 4, resulting in a new element.

$U 238 \to Th 234 + He 42$

In this example, uranium-238 decays to thorium-234 and emits an alpha particle.

Beta (β) Decay

Beta decay occurs in two forms: β– decay and β+ decay (positron emission). Both processes involve the transformation of a nucleon (neutron or proton) into a different type of nucleon, and the emission of a beta particle (electron or positron) and a neutrino (in the case of β– decay) or an antineutrino (in β+ decay).

Beta Minus (β–) Decay

In β– decay, a neutron in the nucleus transforms into a proton, emitting an electron (β–) and an antineutrino. The atomic number increases by 1, but the mass number remains the same.

$n \to p + e - + ν e$

For example, carbon-14 decays by β– decay to nitrogen-14:

$C 14 \to N 14 + e - + ν e$

Beta Plus (β+) Decay (Positron Emission)

In β+ decay, a proton is converted into a neutron, emitting a positron (the antimatter counterpart of the electron) and a neutrino.

$p \to n + e + + ν e$

An example of this is the decay of fluorine-18 in positron emission tomography (PET):

$F 18 \to O 18 + e + + ν e$

Gamma (γ) Decay

Gamma decay involves the emission of high-energy photons (gamma rays) from the nucleus of an atom. This process typically follows other types of decay (such as α or β decay) where the daughter nucleus is in an excited state. The gamma ray emission brings the nucleus back to its ground state.

Example: If a nucleus of technetium-99m (99mTc) undergoes gamma decay, it releases a gamma photon and transitions to a lower energy state:

$Tc 99 \to Tc 99 + γ$