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No, an atom cannot simultaneously contain both an alpha particle and a beta particle. Let's understand the nature of these particles and their relationship to atoms.

An alpha particle is a type of particle consisting of two protons and two neutrons, which is equivalent to a helium-4 nucleus. It carries a positive charge of +2e (where "e" represents the elementary charge). Alpha particles are typically emitted during certain types of radioactive decay, such as alpha decay.

On the other hand, a beta particle refers to either an electron (β-) or a positron (β+). Beta decay occurs when a nucleus undergoes a transformation, emitting either an electron or a positron along with an associated antineutrino or neutrino, respectively. In β- decay, a neutron in the nucleus is converted into a proton, and an electron and an antineutrino are emitted. In β+ decay, a proton is transformed into a neutron, and a positron and a neutrino are emitted.

When an alpha particle or a beta particle is emitted during a radioactive decay process, it carries energy and momentum away from the original atom. The atom undergoes a nuclear transformation to achieve a more stable configuration. As a result, the original atom loses or gains nucleons (protons or neutrons) in the nucleus, and the overall charge and mass of the atom change.

Therefore, at any given time, an atom can have either an alpha particle or a beta particle as a result of a radioactive decay process, but it cannot have both simultaneously. The emission of an alpha or beta particle alters the composition and characteristics of the atom, leading to a different element or isotope.

It's important to note that atoms can undergo various types of radioactive decay processes, and the specific decay mode depends on the nuclide involved. The emission of alpha or beta particles is just one example of the many possible decay pathways for unstable atomic nuclei.

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