No, electrons do not orbit an atom in a classical sense, like planets orbiting the Sun. The classical planetary model of electron orbits was proposed by Niels Bohr but has been replaced by more accurate quantum mechanical models.
According to quantum mechanics, electrons in atoms occupy regions of space called orbitals, which represent the probability distribution of finding an electron at a particular location. Orbitals have specific energy levels and shapes determined by mathematical equations.
The visualization of electrons in orbitals as depicted in diagrams is a way to represent the probability density of finding an electron in a particular region around the nucleus. These representations are based on mathematical models and provide a simplified visualization to aid in understanding atomic structure.
The commonly seen planar representation of orbitals is a simplification used to make the concept more accessible. In reality, orbitals are three-dimensional and can have complex shapes, including lobes and nodes. The planar representation helps to visualize the orientation and relative positions of different orbitals within a given energy level (such as p-orbitals oriented along the x, y, and z axes). However, it should be noted that the actual electron distribution is not confined to a single plane but occupies three-dimensional space.
It's important to understand that the precise behavior of electrons in atoms is described by quantum mechanics and cannot be easily visualized in a classical sense. The orbital diagrams are a useful tool for conceptualizing electron distribution but should not be interpreted as depicting the physical trajectory or path of an electron.