In the photoelectric effect, if the incident photon energy is below the work function, what happens to electrons?

• A. Electrons are ejected with kinetic energy equal to the photon energy
• B. No electrons are ejected
• C. Electrons are ejected with any energy above the work function
• D. Electrons are ejected only if the photon energy exceeds twice the work function

Answer: (B)

The key idea is that an electron can be released only if the incoming photon supplies at least the energy needed to overcome the surface’s binding energy, called the work function. Energy conservation for photoemission is E_photon = φ + KE, where φ is the work function and KE is the electron’s kinetic energy after emission (nonnegative). If the photon energy is less than φ, there isn’t enough energy to liberate the electron, so no emission occurs. That’s why nothing happens to the electrons in this case. When the photon energy is at least φ, electrons are emitted with KE = E_photon − φ. The other scenarios described would require violating energy conservation or assuming a threshold condition that isn’t correct for this situation.