If hf equals the work function φ in the photoelectric effect, what is the kinetic energy of the emitted electrons?

If hf equals the work function φ in the photoelectric effect, what is the kinetic energy of the emitted electrons?

• A. No electrons are emitted
• B. Emitted electrons have some kinetic energy
• C. Emitted electrons have maximum kinetic energy
• D. Emitted electrons have zero kinetic energy

Answer: (D)

Energy conservation in the photoelectric effect tells us that the photon energy hf must overcome the work function φ to free an electron, and any extra energy becomes the electron’s kinetic energy. The relation is KE = hf − φ, with KE representing the maximum kinetic energy of the emitted electrons. If hf equals φ exactly, there’s no extra energy left after lifting the electron out of the surface, so the kinetic energy is zero. In this threshold case, electrons can still be emitted (the energy just suffices to escape), but they have no kinetic energy in this idealized picture. If hf were greater than φ, the emitted electrons would have positive kinetic energy; if hf were less than φ, emission wouldn’t occur at all.

Energy conservation in the photoelectric effect tells us that the photon energy hf must overcome the work function φ to free an electron, and any extra energy becomes the electron’s kinetic energy. The relation is KE = hf − φ, with KE representing the maximum kinetic energy of the emitted electrons.

If hf equals φ exactly, there’s no extra energy left after lifting the electron out of the surface, so the kinetic energy is zero. In this threshold case, electrons can still be emitted (the energy just suffices to escape), but they have no kinetic energy in this idealized picture. If hf were greater than φ, the emitted electrons would have positive kinetic energy; if hf were less than φ, emission wouldn’t occur at all.