Increasing intensity causes a contradiction in classical physics?

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Increasing the intensity of a light source in the photoelectric effect results in a higher number of emitted photoelectrons but does not increase their kinetic energy. Instead, changing the color of the light, which affects its frequency, leads to an increase in the kinetic energy of the emitted electrons. This phenomenon contradicts classical physics, which posits that light intensity correlates with wave amplitude and should not depend on frequency. The discussion highlights the limitations of classical physics in explaining the photoelectric effect, emphasizing the need for quantum mechanics. Understanding this contradiction is crucial for grasping the principles of modern physics.
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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.
 
So I know that electrons are fundamental, there's no 'material' that makes them up, it's like talking about a colour itself rather than a car or a flower. Now protons and neutrons and quarks and whatever other stuff is there fundamentally, I want someone to kind of teach me these, I have a lot of questions that books might not give the answer in the way I understand. Thanks
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