Beta decay is a type of radioactive decay that occurs when an unstable atomic nucleus emits a beta particle, which is essentially an electron. In this context, the beta particle can be represented by the symbol \( e^- \). The electron has an atomic mass that is negligible, often approximated as 0, and its atomic number is -1, reflecting its negative charge, which is the opposite of a proton's positive charge (atomic number +1).
To illustrate beta decay, consider the example of mercury-201 (\( \text{Hg}_{80}^{201} \)). In this case, the atomic mass of mercury is 201, and its atomic number is 80. When mercury-201 undergoes beta decay, it emits a beta particle. The conservation of atomic mass and atomic number must be maintained in the decay process. Since the emitted electron has no mass, the mass of the resulting element remains 201. However, the atomic number changes due to the emission of the electron.
To determine the new atomic number after the emission, we can set up the equation: \( 80 + (-1) = 81 \). This means that the new element formed after the beta decay will have an atomic number of 81, which corresponds to thallium (Tl). Therefore, the complete representation of this beta decay can be written as:
\[ \text{Hg}_{80}^{201} \rightarrow \text{Tl}_{81}^{201} + e^- \]
This equation illustrates the process of beta decay, where mercury-201 transforms into thallium-201 while emitting a beta particle (electron).