Atoms are defined by their core structure. The central nucleus contains positively charged protons and neutrons, which carry no charge. Surrounding this nucleus is a cloud of much lighter, negatively charged electrons.
The properties of any element are determined by two key numbers. The Atomic Number (\(Z\)) is the count of protons, uniquely identifying the element. The Mass Number (\(A\)) is the total count of both protons and neutrons. Atoms with an imbalanced ratio of neutrons to protons are unstable and spontaneously change their nucleus through radioactive decay to achieve stability.
The Mechanism of Beta Decay
Beta decay occurs in atoms containing an excess of neutrons, making them neutron-rich. This process is driven by the weak nuclear force. To correct the neutron-to-proton imbalance, a neutron inside the nucleus converts into a proton.
This change involves the emission of two particles from the nucleus: an electron and an electron antineutrino. The emitted electron is the high-energy beta particle, created at the instant of decay, not ejected from the atom’s surrounding electron shells. The electron antineutrino is a neutral particle with negligible mass, which helps ensure that energy and momentum are conserved. The net result is that the nucleus gains a proton and loses a neutron.
The transformation is summarized as \(n \rightarrow p + e^- + \bar{\nu}_e\). The newly created proton remains within the nucleus, while the electron and antineutrino are ejected at high speed.
Why the Atomic Mass Number Remains Constant
The primary question regarding beta decay concerns the change in atomic mass, which is directly related to the Mass Number (\(A\)). The Mass Number is defined as the total number of particles within the nucleus—the sum of protons and neutrons. In beta-minus decay, a neutron transforms into a proton.
While the identity of the nucleon changes from neutral to positive, the total count of nucleons does not change. You start with one neutron and end with one proton, meaning the total count of heavy particles in the nucleus remains the same. Since the Mass Number (\(A\)) tracks this total count, it is conserved and does not change during the decay.
The emitted beta particle, which is an electron, has an extremely small mass compared to a proton or a neutron. A proton or neutron has a mass of approximately one atomic mass unit. Consequently, the mass contribution of the electron is considered negligible when calculating the Mass Number (\(A\)), which is why the mass number is typically written as \(0\) for a beta particle in nuclear equations. The slight reduction in the actual atomic mass due to the electron’s mass and the mass-energy conversion is negligible for the purposes of the mass number, which is a whole number count.
The Resulting Change in Atomic Identity
Although the Mass Number (\(A\)) stays the same, the identity of the atom fundamentally changes during beta decay. The identity of an element is solely determined by its Atomic Number (\(Z\)), which is the number of protons in the nucleus. Since a neutron converts into a proton, the nucleus now contains one more proton than it did before the decay.
This increase means the Atomic Number (\(Z\)) increases by one unit, a process known as nuclear transmutation. By moving up one position on the periodic table, the original element transforms into a completely different element with distinct chemical properties.
A classic example is the decay of Carbon-14 (\(\text{}^{14}_{6}\text{C}\)), which has six protons. When Carbon-14 undergoes beta decay, one of its eight neutrons turns into a proton. The resulting nucleus now contains seven protons and seven neutrons, giving it a new Atomic Number of seven. An atom with seven protons is no longer carbon, but nitrogen (\(\text{}^{14}_{7}\text{N}\)). The Mass Number remains \(14\) in this example, but the element has changed from Carbon to Nitrogen.