According to classical electrodynamics, an electron at rest does not radiate electromagnetic waves. This is because the emission of electromagnetic radiation, such as light or radio waves, is associated with the acceleration or deceleration of charged particles.
However, when an electron is in motion, it can radiate electromagnetic waves. Accelerating charges generate changing electric and magnetic fields, which then propagate as electromagnetic waves. This phenomenon is described by Maxwell's equations, which are fundamental equations in electromagnetism.
When an electron is in a stable, non-accelerating state or at rest, it does not emit electromagnetic radiation. However, it is worth noting that the concept of an electron being "at rest" is a simplification. Electrons are fundamental particles with an intrinsic property called spin, and according to quantum mechanics, they exhibit particle-wave duality. Even in a stationary state, electrons can still be described by a wave function, which implies a non-zero probability density spread out over space.
Additionally, it's important to mention that the behavior of subatomic particles, including electrons, is better described by quantum mechanics rather than classical electrodynamics. In the quantum realm, particles can exhibit behavior that is fundamentally different from classical physics. Quantum electrodynamics (QED) is the theoretical framework that successfully describes the interaction of electrons and electromagnetic fields, accounting for both particle and wave aspects.
In QED, electrons can interact with virtual photons, which are particles that mediate electromagnetic interactions. These interactions can lead to phenomena such as electron-electron scattering or electron-photon interactions, but they are distinct from the continuous radiation of electromagnetic waves associated with accelerated charges.