Electrons are not stationary around a nucleus, even if it remains in the same excitation state / in the same 'orbit'.
As moving electrons should stir the EM field, they should be creating EM waves/light as well? But that couldn't be as it would mean electrons are constantly losing energy?
The reason quantum mechanics became necessary was because classical mechanics and classical electrodynamics could not explain the black body radiation, the photoelectric effect and, the spectra of atoms.
The classical picture of electrons orbiting around the nucleus has the problem of radiation and neutralization so no atoms could be modeled with electrons around the nucleus. The Bohr model solved this and explained the spectra of atoms, quantizing the angular momentum of the electrons so there would be no continuous radiation, but radiation was obtained only when a photon was emitted from an energy level to a lower energy level.These are the spectra:
The Bohr model has been superseded by the full theory of quantum mechanics, that gives the same results as the arbitrary quantization of the angular momentum of the Bohr model, and opened the study of the microcosm of atoms molecules and lattices and the attendant applications.
BTW electrons are not in orbits, but in orbitals defined by the wavefunction of the particular solution, the probability of being at a specific (r , theta, phi).
