According to classical physics, the reason an electron cannot orbit the nucleus of an atom infinitely is due to the principles of classical electrodynamics and the behavior of charged particles moving in a circular path. This model of electron behavior is known as the Rutherford-Bohr model.
According to classical electrodynamics, an accelerated charged particle, such as an electron moving in a circular orbit, would continuously radiate energy in the form of electromagnetic radiation. This energy loss would cause the electron to spiral inward toward the nucleus, eventually collapsing into it.
If this were the case, atoms would be highly unstable and matter as we know it would not exist. However, this is not what is observed in reality. Experimental evidence shows that atoms are stable and electrons do not simply collapse into the nucleus.
The explanation for this stability comes from quantum mechanics, a more accurate description of the behavior of particles at the atomic and subatomic levels. In quantum mechanics, electrons are described by wave functions that determine their probability distribution around the nucleus. These wave functions have specific energy levels, and electrons occupy these energy levels in discrete quantities.
The allowed energy levels in an atom form what is known as an electron shell structure, and each shell can only accommodate a certain number of electrons. When an electron is in one of these stable energy levels, it does not radiate energy and spiral into the nucleus.
In summary, the inability of an electron to orbit the nucleus infinitely is due to the principles of classical electrodynamics and the energy loss associated with accelerated charged particles. However, the more accurate description provided by quantum mechanics and the concept of electron energy levels explain the observed stability of atoms.