Which equation expresses the photon energy in the photoelectric effect?

• A. E = hf = work function + KE
• B. E = mc^2
• C. p = h/λ
• D. F = ma

Answer: (A)

In the photoelectric effect, the energy of the incoming photon must do two things: supply enough energy to overcome the surface’s work function and provide any remaining energy as the kinetic energy of the emitted electron. That gives the relation hf = φ + KE, where hf is the photon energy, φ is the work function, and KE is the electron’s kinetic energy. This shows exactly how the photon’s energy is partitioned and why the photon energy is expressed as the sum of the work function and kinetic energy. If hf is less than φ, no emission occurs; if hf exceeds φ, the excess energy becomes KE, KE = hf − φ. The other options don’t describe photon energy in this context: rest energy (E = mc^2) is not about photon interactions with matter here, momentum-magnitude form (p = h/λ) describes momentum, and a force equation (F = ma) is unrelated to photon energy.