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Difficulty: MediumPhotoelectric Effect and Work Function

In a photoelectric effect experiment, monochromatic light of frequency ff (where f>f0f > f_0) illuminates a sodium metal surface, causing the emission of photoelectrons with a maximum kinetic energy KmaxK_{\text{max}} and producing a saturation photoelectric current II. If the intensity of the incident light is quadrupled while maintaining the frequency constant, what are the new values of the maximum kinetic energy of the photoelectrons and the saturation photoelectric current?

  1. The maximum kinetic energy remains KmaxK_{\text{max}}, and the saturation current becomes 4I4I.Answer
  2. B
    The maximum kinetic energy becomes 4Kmax4K_{\text{max}}, and the saturation current remains II.
  3. C
    The maximum kinetic energy becomes 4Kmax4K_{\text{max}}, and the saturation current becomes 4I4I.
  4. D
    The maximum kinetic energy remains KmaxK_{\text{max}}, and the saturation current remains II.

Answer

The maximum kinetic energy remains KmaxK_{\text{max}}, and the saturation current becomes 4I4I.
According to Einstein's photoelectric theory, light intensity corresponds to the rate of photon arrival. Quadrupling the intensity quadruples the number of photons striking the surface per second, thereby quadrupling the rate of emitted photoelectrons and resulting in a saturation current of 4I4I. However, individual photon energy depends strictly on frequency (E=hfE = hf). Because frequency remains constant, the maximum kinetic energy of the photoelectrons remains unchanged at KmaxK_{\text{max}}.

Step-by-Step Solution

1
Apply Einstein's photoelectric equation to analyze the maximum kinetic energy.
Kmax=hf−W0K_{\text{max}} = hf - W_0. Since both frequency ff and work function W0W_0 remain constant, KmaxK_{\text{max}} remains unchanged.
Photon energy depends only on frequency (E=hfE = hf), so intensity changes do not affect individual photon energies or the kinetic energy of emitted photoelectrons.
2
Analyze the relationship between light intensity and photoelectric current.
Intensity IlightI_{\text{light}} is proportional to the number of incident photons per second. Quadrupling intensity increases photon flux by a factor of 4, quadrupling photoelectron rate to 4I4I.
Each photon causes the emission of one photoelectron (assuming 100% quantum efficiency), making photoelectric current directly proportional to light intensity.

Key Concept

Independence of photoelectron kinetic energy from light intensity and direct proportionality of photoelectric current to light intensity.
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Topics

Photoelectric Effect and Work Function

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