No, electrons do not orbit the nucleus of an atom in the same way that planets orbit the Sun. This classical "planetary" model of the atom, known as the Rutherford-Bohr model, was proposed in the early 20th century but has since been replaced by a more accurate understanding of atomic structure based on quantum mechanics.
According to quantum mechanics, electrons exist in regions around the nucleus called orbitals. These orbitals are not fixed paths or trajectories like planetary orbits. Instead, they represent the probability distribution of finding an electron in a particular region of space. The behavior of electrons is described by wave functions, and their positions can only be described in terms of probabilities.
The concept of electron orbitals is based on the wave-particle duality of electrons, where electrons exhibit both wave-like and particle-like properties. The exact position and momentum of an electron cannot be simultaneously known due to the Heisenberg uncertainty principle.
In summary, electrons occupy orbitals around the nucleus, but they do not "orbit" in a classical sense. Their behavior is better understood through quantum mechanics and the probabilistic nature of electron distribution.