Question

The existence of a cutoff frequency in the photoelectric effect a) cannot be explained using classical physics. b) shows that the model provided by classical physics is not correct in this case. c) shows that a photon model of light should be used in this case. d) shows that the energy of the photon is proportional to its frequency. e) All of the above.

Short answer

a) The cutoff frequency cannot be explained using classical physics. b) The observation of a cutoff frequency shows that the model provided by classical physics is not correct in this case. c) The observation of a cutoff frequency shows that a photon model of light should be used in this case. d) The cutoff frequency indicates that the energy of a photon is proportional to its frequency. e) All of the above. Answer: e) All of the above.

Step-by-step solution

Statement a: cannot be explained using classical physics.

Classical physics predicts that light energy is directly proportionate to intensity but did not consider the frequency of light as a factor in the photoelectric effect. Since the cutoff frequency is observed experimentally, statement a is true.

Statement b: shows that the model provided by classical physics is not correct in this case.

The experimentally observed cutoff frequency contradicts the predictions of classical physics, pointing to a deficiency in the classical model for the photoelectric effect. Therefore, statement b is true.

Statement c: shows that a photon model of light should be used in this case.

The photon model, proposed by Albert Einstein, can explain the photoelectric effect, including the cutoff frequency. The photon model states that light is made up of discrete particles called photons, which have energy proportional to their frequency. Thus, statement c is true.

Statement d: shows that the energy of the photon is proportional to its frequency.

The cutoff frequency is the result of the minimum energy needed to eject an electron from the material. The energy of a photon is given by the formula E=hf, where E is the energy, h is Planck's constant, and f is the frequency. The photon model can explain the observed cutoff frequency, which means that the energy of a photon is indeed proportional to its frequency. Therefore, statement d is true.

Conclusion

Since statements a, b, c, and d are all true, the correct answer to the exercise is e) All of the above.

Key concepts

Cutoff Frequency

The cutoff frequency in the context of the photoelectric effect represents the minimum light frequency required to eject electrons from a material. Below this frequency, regardless of the light intensity, no electrons are emitted. This phenomenon contradicts classical physics, which predicts that light intensity alone should affect the emission of electrons.

The discovery of the cutoff frequency helped establish that the energy of light depends not just on intensity, but also on its frequency. In practical terms, if the light’s frequency is below the cutoff, the photons don’t have enough energy to dislodge an electron from the material’s surface.

Classical Physics Limitations

Classical physics suggests that energy is a continuous variable, and that light's energy is directly proportional to its intensity. This would imply that given sufficient time, light of any frequency should eventually cause electrons to be emitted if its intensity is high enough. However, experiments on the photoelectric effect exhibited clear limitations to these classical concepts.

These experiments showed that intensity only affects the number of electrons ejected, not their ability to eject in the first place. This leads to the conclusion that classical models are not suitable for explaining the behavior of light and electrons at atomic scales, giving way to quantum theories.

Photon Model of Light

The photon model of light emerged from the inadequacies of classical physics to explain observations like the photoelectric effect. In this model, light is described as being made up of tiny 'packets' or quanta of energy, known as photons.

The photon model postulates that each photon carries a discrete amount of energy that is proportional to the light's frequency. This quantization explains the cutoff frequency, as only photons with a frequency high enough possess the requisite energy to eject electrons. Albert Einstein’s explanation of the photoelectric effect using the photon model earned him the Nobel Prize in Physics and helped solidify the quantum mechanical understanding of light.

Energy-Frequency Relationship

At the core of the photoelectric effect's resolution is the energy-frequency relationship, expressed in the equation \( E = hf \), where \( E \) is the energy of a photon, \( h \) is Planck's constant, and \( f \) is the frequency of the light.

This equation encapsulates one of the fundamental postulates of quantum mechanics, establishing energy quantization in photons and revealing a direct proportionality between energy and frequency. High frequency (and therefore high energy) photons can eject electrons, reinforcing the relationship's critical role in explaining the photoelectric effect as well as many other quantum phenomena.