When the frequency of the incident light is less than the threshold frequency

Question

BlackTom AI · Accepted Answer

If the incident photon frequency ν is less than the threshold frequency ν0, then each photon does not have enough energy to free an electron from the metal.

1) Relevant knowledge points and concepts
- Photoelectric effect and Einstein’s photoelectric equation: K_max = hν − φ, where K_max is the maximum kinetic energy of emitted electrons, h is Planck’s constant, ν is the photon frequency, and φ is the work function of the metal. The threshold frequency ν0 satisfies φ = hν0. If ν < ν0, the photon energy hν < φ.

2) Step-by-step reasoning
- Start from Einstein’s equation: K_max = hν − φ.
- Substitute φ = hν0: K_max = hν − hν0 = h(ν − ν0).
- If ν < ν0 then (ν − ν0) is negative, so K_max < 0.

3) Intermediate calculation example
- Take ν = 0.8 ν0 (as a concrete example): K_max = h(0.8ν0 − ν0) = h(−0.2ν0) = −0.2 hν0 < 0. A negative kinetic energy is nonphysical, which indicates no electrons are emitted.

4) Why the correct answer is correct
- Because photon energy is insufficient to overcome the work function, no electrons can be ejected regardless of light intensity. Photoelectric emission requires hν ≥ φ; below threshold there is simply no photoelectric current.

5) Why the other choices are incorrect
- b (velocity of photoelectrons is large): impossible because no electrons are emitted, so there is no photoelectron velocity.  
- c (a large photoelectric current is produced): incorrect because current requires emitted electrons; with ν < ν0 none are emitted.  
- d (a little photoelectric current is produced): also incorrect for the same reason; intensity cannot compensate for insufficient photon energy in the classical photoelectric effect.

Conclusion: Therefore, the correct choice is (a) no photoelectric current is produced, which matches the provided answer.

When the frequency of the incident light is less than the threshold frequency单项选择题

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