Which equation gives the energy E of a photon in terms of its frequency f or wavelength λ?

• A. E = h f = h c / λ
• B. E = m c^2
• C. E = p v
• D. E = h λ

Answer: (B)

Photons carry energy in discrete quanta that are proportional to frequency. The fundamental relation is E = h f, where h is Planck's constant. Since frequency and wavelength are linked by f = c/λ, you can also write E = h c / λ. This shows why energy grows with increasing frequency or, equivalently, with decreasing wavelength.

Photons have zero rest mass, so the rest-energy formula E = m c^2 does not describe a photon's energy. The rest-energy applies to particles with mass when they’re at rest, which photons cannot be. The other expressions don’t match how photon energy behaves: E = h λ would imply energy increases with wavelength, which is the opposite of the correct relation, and E = p v isn’t the standard way to express energy for light (for a photon, E = p c, and with p = h/λ that again gives E = h c / λ).