Final answer:
The speed of a photon remains constant regardless of changes in its energy. An increase in a photon's energy results in an increase in frequency and a decrease in wavelength, but not a change in speed.
Step-by-step explanation:
If a photon's energy is increased by a factor of two, its speed in a vacuum remains unchanged. According to Einstein's theory of relativity, the speed of light in a vacuum is constant and does not depend on the energy of the photons. Instead, if a photon's energy is doubled, this affects its frequency and wavelength. The energy of a photon is given by the equation E = hf, where E is energy, h is Planck's constant, and f is the frequency.
Therefore, if the energy E is increased by a factor of two and h remains constant, the frequency must also double. As for the wavelength, because the speed of light c is constant and given by c = λf (where λ is the wavelength), an increase in frequency would lead to a corresponding decrease in wavelength. So, the correct answer is that a photon's speed will remain unchanged, its frequency will increase, and its wavelength will decrease.