Conceptual Questions on the Photoelectric Effect

Problem Statement

Answer the following conceptual questions:

1. Why does increasing the intensity of light below the threshold frequency still fail to eject electrons?
2. How would the stopping potential change if you switched to a light source with higher frequency but the same intensity?
3. What happens to the photocurrent when you decrease the intensity of light while keeping the frequency above threshold?
4. Why does the photoelectric effect provide evidence for the particle nature of light?
5. Does the time delay between shining light and observing emission depend on intensity?

Given / Required

Use the standard quantum explanation: electron binding energy is characterized by the work function, energy of a photon is hf, and electrons escape if hf exceeds the work function.

Hint

Focus on energy per photon rather than total beam energy. Relate stopping potential to maximum kinetic energy of emitted electrons.

Step-by-Step Solution

1. Increasing intensity increases the number of incoming photons but not their individual energy. If hf is below the work function, no single photon provides enough energy, so no electrons escape regardless of how many arrive.
2. Higher frequency means higher photon energy; thus kinetic energy of emitted electrons increases. Stopping potential grows linearly with frequency above threshold, so the required potential becomes more negative (larger magnitude).
3. Lower intensity means fewer photons arriving per second. Since each photon can still eject an electron, the photocurrent decreases proportionally, but the maximum kinetic energy of emitted electrons stays the same.
4. The instant emission with no measurable delay and the dependence on hf rather than intensity indicate that energy arrives in discrete packets. A wave theory would predict gradual energy build-up, which is not observed.
5. Experiments show essentially zero delay (few femtoseconds) because a single photon interaction is enough. The delay does not depend on intensity so long as at least one photon is present; it depends only weakly on material specifics.

Final Answer

• Threshold behavior depends on photon energy, not on total beam intensity.
• Stopping potential increases with frequency because electrons leave with more kinetic energy.
• Photocurrent tracks intensity (number of photons per second) but not stopping potential.
• Photoelectric data supports quantized light.
• The emission is prompt and independent of intensity.

Extension / Variation

• Consider different metals with varying work functions and repeat the reasoning.
• Link the graph of stopping potential vs frequency to Planck’s constant.

Key Concept Recap

• Photon energy hf must exceed the work function for emission.
• Intensity controls photocurrent; frequency controls kinetic energy.
• The effect demonstrates light’s particle nature.