Summary

Quantum theory developed because classical physics can't explain atomic spectra, blackbody radiation or photoelectric effect.
Photons are electrically neutral massless particles.
E=hf, with h being Planck's constant.
Photons travel at c= 299792458 m/s (or c=3*10^8 for simplification) in a free space, and are slowed by a factor of the medium's index of refraction.
Particles like electrons show wave behavior, quantified by de Broglie wavelength \lambda=h/p. Wavelength increases as momentum decreases.
Quantum effects matter when a particles de Broglie wavelength is comparable to the system.
In bound systems, energy and momentum are discrete.