Forces and Motion, Quantum QWC practice question

Question

Expected physics points

• Photoelectric effect involves emission of electrons from a metal surface when light shines on it.
• The wave model predicts that electron emission should depend on the intensity of light, with higher intensity leading to more energetic electrons and emission at any frequency given enough time.
• However, observations show that electron emission only occurs if the incident light's frequency is above a certain threshold frequency (f₀), regardless of intensity.
• Below f₀, no electrons are emitted, even for very high intensities or prolonged exposure.
• The kinetic energy of emitted electrons (photoelectrons) depends on the frequency of the incident light, not its intensity.
• The rate of electron emission is proportional to the intensity of light, provided the frequency is above f₀.

Mark scheme points

• Photoelectric effect involves emission of electrons from a metal surface when light shines on it.
• The wave model predicts that electron emission should depend on the intensity of light, with higher intensity leading to more energetic electrons and emission at any frequency given enough time.
• However, observations show that electron emission only occurs if the incident light's frequency is above a certain threshold frequency (f₀), regardless of intensity.
• Below f₀, no electrons are emitted, even for very high intensities or prolonged exposure.
• The kinetic energy of emitted electrons (photoelectrons) depends on the frequency of the incident light, not its intensity.
• The rate of electron emission is proportional to the intensity of light, provided the frequency is above f₀.

Indicative content

• The photoelectric effect is the emission of electrons from a metal surface when electromagnetic radiation (light) shines on it.
• The wave model of light predicts that the energy carried by a wave is spread out continuously and depends on its intensity. Therefore, it would predict that:
• - Electron emission should occur at any frequency, provided the intensity is high enough or the exposure time is long enough for sufficient energy to accumulate.
• - The kinetic energy of the emitted electrons should increase with increasing light intensity.
• However, experimental observations contradict these predictions:
• - There is a threshold frequency (f₀) below which no electrons are emitted, regardless of the intensity or duration of the incident light.
• - Above the threshold frequency, electrons are emitted instantaneously, even at very low intensities.
• - The maximum kinetic energy of the emitted electrons (photoelectrons) depends on the frequency of the incident light, not its intensity.
• - The rate of electron emission (number of photoelectrons per second) is proportional to the intensity of the incident light, provided its frequency is above f₀.
• These observations are explained by the particulate (photon) model of electromagnetic radiation:
• - Light consists of discrete packets of energy called photons, each with energy E = hf, where h is Planck's constant and f is the frequency.
• - Photoelectric emission is a one-to-one interaction: a single photon interacts with a single electron.
• - For an electron to be emitted, the photon's energy (hf) must be greater than the work function (Φ) of the metal, which is the minimum energy required to remove an electron from the surface.
• - If hf < Φ, the photon does not have enough energy to eject an electron, explaining the threshold frequency.
• - Any excess energy (hf - Φ) is converted into the kinetic energy of the emitted electron: KEmax = hf - Φ. This explains why KEmax depends on frequency, not intensity.
• - Increasing the intensity of light (above f₀) means more photons per second, leading to more one-to-one interactions and thus a higher rate of electron emission, but not more energetic electrons.