Final answer:
The energy of a photon is dependent on its frequency, as described by the equation Ef = hf, with 'E' representing energy and 'f' the frequency. Amplitude and speed do not affect a photon's energy.
Step-by-step explanation:
The energy of a photon depends on its frequency. According to the quantum theory of light, specifically in the work of Albert Einstein, a photon carries an energy quantum that is proportional to its frequency. This relationship is given by the equation Ef = hf, where E represents energy, f is the frequency, and h is Planck's constant. Therefore, when considering the factors that influence a photon's energy, amplitude and speed are not relevant; the speed of all photons in a vacuum is the speed of light, c, and amplitude is linked to the intensity of a wave, not the energy of individual photons.
Regarding parts of electromagnetic wave behavior, the frequency and wavelength are inversely related, but this relationship does not affect the speed, which is constant for electromagnetic waves in a vacuum. Consequently, the only correct answer from the provided options is b. frequency