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

Because each photon carries energy E = hf, if hf is less than the metal’s work function (φ) a single photon cannot free an electron.

1. Relevant concepts
- Photon energy: E_photon = h f (h = Planck’s constant, f = light frequency).
- Work function φ: minimum energy to eject an electron from the metal.
- Photoelectric emission requires E_photon ≥ φ for single-photon emission.
- Light intensity relates to photon flux: Intensity I = (number of photons per second N) × (h f) (per unit area).

2. Step-by-step reasoning
- Given: infrared light initially emits no electrons → therefore hf (infrared) < φ.
- Increase intensity means increasing N (more photons per second) while f (and thus hf) remains the same.
- Each photon still has energy hf < φ, so a single photon still cannot eject an electron.

3. Intermediate calculations (symbolic)
- Photon energy: E_photon = h f.
- Threshold condition: emission if and only if h f ≥ φ.
- Photon flux: N = I / (h f). Increasing I increases N, but not h f.
- Since h f < φ, no single-photon ejection: emission rate ≈ 0.

4. Why the correct answer is correct
Quantum theory predicts electron emission depends on individual photon energy, not merely total intensity. If photons lack the required energy, adding more such photons (raising intensity) does not overcome the work function, so the photoelectric current remains essentially zero.

5. Why other options are incorrect
- a/b (current increases immediately or gradually): would be correct only if hf ≥ φ, because extra photons produce more emitted electrons. Not applicable here.
- c/d (current decreases): increasing intensity cannot reduce emission from zero to negative; no physical basis.
- f (cannot be determined): it is determinable by comparing hf to φ; here we know hf < φ so prediction is definite.

6. Conclusion
Therefore the quantum prediction is that there is no change in the photoelectric current, matching 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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