Electrons do not spontaneously emit photons in the absence of external interactions or transitions between energy states. In classical electrodynamics, an accelerating charged particle, such as an electron, would emit electromagnetic radiation (photons) due to its acceleration. However, in the context of quantum mechanics, the emission of photons by electrons is governed by specific processes, such as electron transitions in atoms or scattering interactions.
In atomic systems, electrons can transition between different energy levels, emitting or absorbing photons in the process. The number of photons emitted or absorbed in a given transition depends on the specific energy difference between the initial and final states involved. These transitions follow the laws of quantum mechanics, and their probabilities can be calculated using methods such as quantum electrodynamics.
Regarding the distribution of the numbers of photons emitted by electrons, it would depend on the specific physical system and the conditions under which the emission occurs. The distribution can vary widely, ranging from discrete numbers for specific transitions to continuous distributions for certain processes like bremsstrahlung radiation. Additionally, the distribution can be affected by factors such as temperature, energy levels involved, and the presence of other particles or fields.
In general, it is not accurate to attribute a definite number of photons emitted by an electron in a given timeframe without considering the specific context and interaction involved. The number of photons emitted by electrons can be quantified and predicted for specific scenarios, but a universal distribution applicable to all electrons is not feasible due to the variety of possible interactions and energy states.