Electromagentic Radiation by objects at rest 
When electrically charged particle moves under acceleration, it emits electromagnetic radiation.

So, the question is that when an electrically-charged particle, say a proton or an electron is at rest, then it will emit no EM radiation?
 A: Accelerating charged particles, electrons or protons, emit electromagnetic waves. This means if they are moving with a constant velocity, or they are stationary, they will not  emit electromagnetic radiation (photons).
An electron in an atom (in an excited state) can emit a photon, and drops to a lower energy level.
But a free, isolated, non-accelerating electron will not spontaneously emit a photon, because conservation of momentum/energy will not hold.
Also, a proton (in a nucleus) can go through a different radiative process, called beta decay where a proton decays into neutron with the emission of a positron and a neutrino. And a free proton does not spontaneously decay (as far as all experiments have shown).
Also, at the macroscopic level, large material objects emit thermal electromagnetic waves, or thermal radiation. This is because again, the charged protons and electrons (in the atoms that make up a macroscopic object), are constantly vibrating. When these charged particles vibrate, since they are being rapidly accelerated and decelerated, they will emit these electromagnetic waves. Again, an acceleration of charged particles is required for the emission of electromagnetic waves.
