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Difficulty: MediumPhotoelectric Effect and Work Function

A beam of monochromatic light strikes a photosensitive metal surface, causing the emission of photoelectrons. If the intensity of the incident light is doubled while maintaining the same frequency, what happens to the stopping potential of the emitted electrons?

  1. It remains unchangedAnswer
  2. B
    It is doubled
  3. C
    It is quadrupled
  4. D
    It is reduced by half

Answer

The stopping potential remains unchanged because it depends only on the frequency of the incident light, not its intensity.
According to Einstein's photoelectric theory, the maximum kinetic energy of emitted electrons is given by Kmax=hf−W0K_{\text{max}} = hf - W_0, where hh is Planck's constant, ff is the frequency of the incident light, and W0W_0 is the work function of the metal. The stopping potential VsV_s is related to KmaxK_{\text{max}} by eVs=Kmaxe V_s = K_{\text{max}}. Doubling the intensity of the light increases the number of photons hitting the surface per unit time (thus increasing the photocurrent), but it does not change the energy of individual photons (hfhf). Consequently, the maximum kinetic energy and the stopping potential remain completely unchanged.

Step-by-Step Solution

1
Recall Einstein's photoelectric equation
Ekmax=hf−W0E_k^{\text{max}} = hf - W_0
The maximum kinetic energy of emitted photoelectrons depends directly on the photon energy (hfhf) and the work function (W0W_0) of the metal.
2
Relate maximum kinetic energy to stopping potential
eVs=Ekmax=hf−W0  ⟹  Vs=hf−W0ee V_s = E_k^{\text{max}} = hf - W_0 \implies V_s = \frac{hf - W_0}{e}
Stopping potential (VsV_s) is directly proportional to the maximum kinetic energy.
3
Analyze the effect of changing light intensity at constant frequency
Increasing intensity increases the number of photons per second (and thus the photocurrent), but does not alter the energy of individual photons (hfhf). Therefore, VsV_s remains constant.
Intensity affects electron rate emission, not individual electron energy.

Key Concept

Independence of photoelectron kinetic energy and stopping potential from light intensity
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Topics

Photoelectric Effect and Work Function

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