I'm just starting to learn physics and I have a question (that is probably stupid.)
I learned that energy levels that the bound electron can have are discrete. I also learned that when an electron transitions from one level to another, a photon with a specific wavelength (energy) is created and released into the wild.
My question is this: are there holes in the electromagnetic spectrum, values of frequency that the created photon can't possibly have?
No, there aren't any holes like that in the EM spectrum.
There are other ways of creating photons than by having electrons bound in atoms transition from one level to another. (For example, you can create pretty much any frequency of photon you want by accelerating a free electron.)
The other answers are correct, but I think they miss one important point.
The energy levels are not really discrete, because:
Frequencies are not exactly defined. Due to the Heisenberg uncertainty principle, the location and frequency of a photon cannot both be exactly determined. Therefore, emission (and absorption) does not happen at an exact frequency, but at a finite range of frequencies. This is called natural broadening.
Next, molecules do not exist in isolation. They collide with other molecules, which again changes the energy levels. This is called pressure broadening.
Next, molecules are not stationary, but are quickly moving. This also causes the energy levels (absorption/emission lines) to broaden. This is called thermal broadening.
The latter two are much stronger than the first one (at least in the Earth's atmosphere), but the first one is very fundamental as well. Energy levels are not really discrete. Therefore, the electromagnetic spectrum is not, either.
You mention that the energy levels of a bound electron are discrete. Have you considered the energy levels of a unbound electron? In this case, the energy levels are not discrete, but rather continuous and can take on any frequency.
Even if a photon is created by the transition of electrons in an atom, if the atom is moving relatively to the observer, the Doppler shift changes the frequency. In principle, any frequency can be obtained like this.
