Ultraviolet light shined on a metal initially emits electrons. What is the quantum prediction if the intensity of the light is increased?

Question

BlackTom AI · Accepted Answer

Photons deliver discrete energy hν to electrons, so the photoelectric effect must be analyzed in terms of photon flux and single-photon absorption.

1. Relevant knowledge points and concepts
- Photoelectric effect (quantum view): each incoming photon of frequency ν can eject at most one electron if hν ≥ Φ (work function).  
- Intensity of light: classically energy per unit area per unit time; quantum mechanically it is proportional to the number of photons arriving per second (photon flux) times hν.  
- Photocurrent: proportional to the number of electrons ejected per second that reach the anode (Iphoto = e · rate_electrons).  
- Kinetic energy of emitted electrons (KEmax) = hν − Φ, independent of intensity.

2. Step-by-step reasoning
- Assume ultraviolet light already has hν ≥ Φ so electrons are emitted.  
- Increasing the intensity at the same frequency increases the number of photons per second incident on the metal (photon flux increases).  
- Each additional photon can produce another emitted electron (neglecting saturation and secondary processes), so the electron emission rate increases immediately.  
- Photocurrent is proportional to the emission rate, so it increases immediately when intensity increases.

3. Calculations and intermediate steps
- Intensity S = (number of photons per second) · hν / area. Let n be photon rate incident; then S ∝ n·hν.  
- Electron emission rate ≈ η·n (η = quantum efficiency).  
- Photocurrent I = e·(η·n). If intensity doubles (n → 2n), then I → 2I. This change is instantaneous with the change in photon flux.

4. Why the correct answer is correct
- Quantum theory predicts an immediate increase in photocurrent because more photons per unit time immediately produce more emitted electrons; there is no required accumulation time.

5. Why other options are incorrect
- “Gradually” implies a time delay or buildup; experiments show essentially no measurable delay for ultraviolet frequencies above threshold.  
- “Decreases” or “no change” contradict the direct proportionality between photon flux and emission rate (unless frequency is changed below threshold or saturation/clamping occurs, which is not stated).  
- “Cannot be determined” is false because the quantum prediction is well-defined.

6. Conclusion
Therefore the photocurrent increases immediately when intensity is increased, confirming answer a.

Ultraviolet light shined on a metal initially emits electrons. What is the quantum prediction if the intensity of the light is increased?单项选择题

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