Increasing intensity causes a contradiction in classical physics?

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Turion
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According to my prof, increasing intensity of the light source in a photocell for the photoelectric effect does not increase the kinetic energy of photoelectrons emitted. Instead, the number of electrons emitted (and current) increases. Changing the colour of the light causes an increase in kinetic energy of the photoelectrons emitted.

Why is this a contradiction in classical physics as my prof claims?
 
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Classical physics states that the intensity of light should be proportional to the square of the amplitude of the wave and should have nothing to do with its frequency.