The model that illustrates the arrangement of electrons around an atom's nucleus is known as the Bohr model or the quantum mechanical model. The Bohr model depicts electrons in specific orbits around the nucleus, correlating energy levels to these orbits. In the quantum mechanical model, however, electrons are described as existing in probability clouds or orbitals, rather than fixed paths. This model accounts for complex behaviors of electrons, such as electron configurations and chemical bonding, revolutionizing our understanding of atomic structure.