It is not possible to increase the energy of the electron by increasing the intensity of the radiation,
since the electron will still interact with only one photon. The only way to generate more energetic
photons is by using light of a higher frequency, that is light with more energetic photons. This phenomenon
cannot be explained by the classical physics, in which the radiation is an electromagnetic
wave.
http://fy.chalmers.se/~torkel/Teaching/Astro_proc/lecture4.pdf
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