Infrared light shined on a metal initially emits no electrons. What is the quantum prediction if the intensity of the light is increased?

Question

BlackTom AI · Accepted Answer

Photon energy is E = hf, so each photon must have energy at least equal to the metal’s work function Φ to eject an electron (photoelectric effect). Intensity controls the number of photons arriving per second, not the energy per photon.

1) Relevant concepts
- Photoelectric cutoff: emission occurs only if hf ≥ Φ (threshold frequency).  
- Intensity ∝ number of photons per second × energy per photon (I ∝ N·hf).  
- In the usual quantum photoelectric picture, electrons absorb single photons; increasing N increases current only if individual photons have enough energy to liberate electrons.

2) Step-by-step reasoning
- Infrared light in the scenario initially emits no electrons, so hf_IR < Φ.  
- Increase the intensity: this raises N (photons/sec) but does not change f (photon frequency) or hf.  
- Because each photon still has energy hf_IR < Φ, no single-photon photoemission events occur, so no photoelectric current appears.

3) Intermediate relations/calculation
- E_photon = hf. Given E_photon < Φ initially.  
- Intensity change: I_new = N_new·hf. Even if N_new ≫ N_old, hf remains the same and still < Φ, so emission condition hf ≥ Φ is never met. Thus no electrons are produced.

4) Why this answer is correct
- The quantum (Einstein) explanation predicts zero photoelectric current whenever photon energy is below the work function, regardless of how many such photons arrive per second. Increasing intensity cannot make sub-threshold photons singly eject electrons.

5) Why the other options are incorrect
- (a) and (b): these imply current appears/increases; impossible because photon energy is still below threshold.  
- (c) and (d): current cannot decrease from zero due to increased intensity.  
- (f): the effect is determinable by the photon-energy threshold condition, so this is incorrect.

6) Conclusion
Because hf for the infrared photons remains less than the metal’s work function even after increasing intensity, the quantum prediction is that there is no change in the photoelectric current. This confirms answer e.

Infrared light shined on a metal initially emits no electrons. What is the quantum prediction if the intensity of the light is increased?单项选择题

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