Physics

Problem

Monochromatic light of frequency

0.90f_{\text{th}}

(where

f_{\text{th}}

is the metal’s threshold frequency) shines on a clean metal surface. The intensity of the light is steadily increased by a factor of 100. Which outcome is most consistent with the photoelectric effect? a) Electrons begin to be emitted once the intensity is high enough because they can add the energies of multiple photons. b) No electrons are emitted at any intensity because each photon lacks sufficient energy to overcome the work function. c) Electrons are emitted, and the emission rate increases with intensity while their maximum kinetic energy remains unchanged. d) Electrons are emitted only after a measurable time delay, during which an electron absorbs enough energy from successive photons.

Intuitive explanation

The photoelectric effect depends on photon energy, not light intensity. Since each photon has energy $E = hf$ , and your frequency is below the threshold ( $0.90f_{\text{th}}$ ), no individual photon carries enough energy to eject an electron—no matter how many photons arrive per second. Increasing intensity just means more of these insufficiently energetic photons hit the surface, but that doesn't change what each photon can do. The key insight is that the photoelectric effect is fundamentally a one-photon process where frequency matters, not intensity.

Intuitive explanation

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