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According to Einstein's photoelectric equation, the slope of the plot of kinetic energy of the photoelectrons Vs. the frequency of the incident radiation :

  • A.will depend upon the nature of the metal that emits the photoelectrons
  • B.will depend on the intensity of the incident radiation
  • C.will depend on both the intensity of the radiation and the nature of the metal
  • D.will be the same for all metals and independent of intensity of radiation

Answer: D

The slope will be the same for all metals and independent of intensity of radiation.

Einstein's equation is

\[ KE_{\max} = h\nu - \phi \]

A plot of KE against ν is a straight line of slope h, Planck's constant, for every metal. The metal changes only the work function φ, which moves the intercept and the threshold frequency, not the slope. Intensity changes only the number of photoelectrons.

That rules out options A, B and C, which all make the slope depend on the metal or the intensity.

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