You are correct that all photons, regardless of their color or frequency, travel at the same speed in a vacuum, which is approximately the speed of light. However, the energy of a photon is directly related to its frequency or color of light.
In physics, energy is quantized in discrete units known as "quanta" or "packets." Photons are the quanta of light, and their energy is proportional to their frequency. The higher the frequency of a photon, the greater its energy.
The relationship between the energy (E) of a photon and its frequency (ν) is given by the equation E = hν, where h is Planck's constant. This equation, known as the Planck-Einstein relation, describes the fundamental relationship between energy and frequency in quantum mechanics.
So, different colors or frequencies of light correspond to different amounts of energy carried by photons. For example, blue light has a higher frequency and, therefore, more energy per photon than red light. This difference in energy is what allows blue light to have a greater potential for causing certain effects, such as ionizing atoms or stimulating certain biological processes, compared to red light.
It's important to note that while all photons travel at the same speed in a vacuum, their energy can vary based on their frequency or color, as determined by the electromagnetic spectrum.