When an atom releases both an alpha particle and a beta particle simultaneously, the resulting change in the atomic number depends on the specific elements involved and their respective decay processes. Let's consider a general scenario to understand the potential changes.
An alpha particle consists of two protons and two neutrons, so it has a mass number of 4 and an atomic number of 2 (equivalent to a helium nucleus). On the other hand, a beta particle can be either an electron (β-) or a positron (β+). In this case, we'll assume it's an electron (β-) emitted during beta-minus decay.
During alpha decay, an atom emits an alpha particle and reduces its atomic number by 2 and its mass number by 4. For example, if we consider a hypothetical atom with an initial atomic number of Z and an initial mass number of A, the alpha decay process would result in a final atomic number of Z-2 and a final mass number of A-4.
During beta-minus decay, an atom emits an electron (beta particle) and increases its atomic number by 1 while retaining the same mass number. Therefore, if we consider the same hypothetical atom undergoing beta-minus decay simultaneously with alpha decay, the net effect would be a decrease of 1 in the atomic number (Z-1) and a decrease of 4 in the mass number (A-4).
It's worth noting that simultaneous alpha and beta decay is relatively rare, and most radioactive isotopes undergo either alpha decay or beta decay individually. Additionally, the specific changes in the atomic number and mass number depend on the isotopes involved and their decay properties.