Radioactive decay is the process by which an unstable atomic nucleus spontaneously transforms to achieve a more stable configuration. This transformation results in the emission of radiation, leading to a change in the identity of the atom. The identity of any chemical element is determined by its atomic number (\(Z\)), which represents the count of protons found within the nucleus. Beta decay is a common mechanism through which many neutron- or proton-imbalanced nuclei undergo this conversion.
Understanding Atomic Structure and Beta Particles
An atom’s nucleus is characterized by two numbers: the atomic number (\(Z\)) and the mass number (\(A\)). The mass number (\(A\)) represents the total count of protons and neutrons (nucleons) in the nucleus. The atomic number (\(Z\)), or proton count, defines the element’s chemical properties and its place on the periodic table.
The beta particle is a high-energy, fast-moving particle emitted from the nucleus during radioactive decay. This particle is not an original component of the nucleus. Instead, it is newly created at the moment of the nuclear transformation. The beta particle is symbolized either as the Greek letter \(\beta\) or as an electron (\(e^-\)) or positron (\(e^+\)).
The Mechanism of Beta Minus Decay
Beta minus (\(\beta^-\)) decay is the most common form of beta decay, occurring in nuclei with an excess of neutrons relative to protons. In this process, a neutron converts into a proton, an electron, and an electron antineutrino (\(\bar{\nu}\)). The newly formed proton remains inside the nucleus, while the electron and the antineutrino are ejected.
Because the nucleus gains one proton, the atomic number (\(Z\)) increases by one unit, changing the element’s chemical identity. For example, carbon-14 undergoes beta minus decay to become nitrogen-14.
The mass number (\(A\)) remains unchanged during this conversion because a neutron (mass number 1) is replaced by a proton (mass number 1). This transformation shifts the nucleus toward a more stable neutron-to-proton ratio by reducing the neutron count by one and increasing the proton count by one. The process is represented as \(n \rightarrow p + e^- + \bar{\nu}\).
The Mechanism of Positron Emission
Nuclei that are proton-rich often undergo positron emission, or beta plus (\(\beta^+\)) decay. Here, the conversion is reversed: a proton transforms into a neutron, a positron, and an electron neutrino (\(\nu\)). The positron is the antimatter equivalent of an electron, possessing the same mass but a positive electrical charge.
When the proton converts into a neutron, the nucleus loses one positive charge, resulting in the atomic number (\(Z\)) decreasing by one unit. The resulting neutron stays in the nucleus, and the emitted positron and neutrino escape. For instance, a fluorine-18 nucleus undergoes positron emission to become an oxygen-18 nucleus.
The mass number (\(A\)) remains unchanged because the total number of nucleons is constant. This decay corrects the imbalance by reducing the proton count and increasing the neutron count by one.
How to Write and Balance Nuclear Equations
The changes in atomic identity and number are documented using a nuclear equation, which must obey conservation laws. The rule for balancing these equations is that the sum of the mass numbers (\(A\)) on the reactant side must equal the sum on the product side. Similarly, the sum of the atomic numbers (\(Z\)) on the reactant side must equal the sum on the product side.
In standard notation, the mass number (\(A\)) is placed at the top left of the element symbol, and the atomic number (\(Z\)) is placed at the bottom left.
For a \(\beta^-\) decay, like carbon-14 to nitrogen-14, the atomic number balancing is \(6 = 7 + (-1)\), where the electron (\(\beta^-\)) has an atomic number of \(-1\). The mass numbers balance because \(14 = 14 + 0\).
Conversely, in a \(\beta^+\) decay, such as carbon-11 to boron-11, the balancing requires the positron (\(\beta^+\)) to have an atomic number of \(+1\). The atomic number balancing is \(6 = 5 + (+1)\), while the mass number remains balanced at \(11 = 11 + 0\). This representation confirms that nuclear reactions conserve the total number of nucleons and the total charge.