Which particle has no mass and carries a discrete amount of energy?

The photon is the correct choice because it is a fundamental particle of light that is massless and is responsible for electromagnetic radiation. Photons travel at the speed of light and carry energy that is proportional to their frequency, as described by the equation E = hf, where E is energy, h is Planck's constant, and f is the frequency. This property distinguishes photons from other particles that have mass, such as electrons, neutrons, and protons.

Electrons, neutrons, and protons all have rest mass; therefore, they cannot be considered massless particles. Neutrons and protons, in particular, are baryons and while they are integral to atomic structure, they possess significant mass and don't carry energy in the form of electromagnetic radiation like photons do. Electrons, while they do carry charge and energy, still have a measurable mass. Thus, the photon is unique in that it carries energy without possessing any mass.