No electrons are emitted from metal surfaces below ____________ frequency.

Question

BlackTom AI · Accepted Answer

Photoelectric effect requires photons with energy at least equal to the metal’s work function, so no electrons are emitted if the incident photon energy is too small.

1. Relevant knowledge points and concepts
- Photon energy: E = hf, where h is Planck’s constant and f is frequency.
- Work function (φ): minimum energy needed to free an electron from the metal.
- Photoelectric condition: emission occurs only when hf ≥ φ.
- Threshold frequency (f0): the minimum frequency satisfying hf0 = φ.

2. Step-by-step reasoning
- Start with photon energy: E_photon = h f.
- The maximum kinetic energy of an emitted electron is K_max = hf − φ (Einstein’s photoelectric equation).
- If hf < φ then K_max would be negative, which is physically impossible, so no electrons are emitted.
- Therefore emission requires f ≥ f0 where f0 = φ/h.

3. Intermediate steps and simple calculation form
- Set equality at threshold: h f0 = φ.
- Solve for threshold frequency: f0 = φ / h.
- For any f < f0, hf − φ < 0 ⇒ no emission.

4. Why the correct answer is correct
- "Threshold" frequency is the established term in photoelectric theory meaning the minimum frequency required for electron emission. It directly follows from hf = φ, so below f0 no electrons are emitted.

5. Why other options are incorrect
- a. angular: refers to angular frequency (ω = 2πf), not the specific physical cutoff; the phenomenon is described in terms of ordinary frequency and the term “angular frequency” is not the standard threshold condition.
- c. maximum: implies an upper bound, but emission fails below a minimum, not above a maximum.
- d. minimum: while “minimum” loosely describes the idea, the precise and standard term used in physics is “threshold” frequency.

6. Conclusion
This reasoning confirms the correct choice is "threshold," matching the provided answer.

No electrons are emitted from metal surfaces below ____________ frequency.单项选择题

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