(a) According to the classical wave theory, the intensity (I) of light (which is a transverse electro magnetgic wave according to Maxwells equations) is directly proportional to the square of its amplitude (A).
Therefore, increasing intensity means increasing the wave amplitude. Hence, it is conceivable that if incident light intensity is increased, electrons in the metal will oscillate more violently and will be ejected with higher kinetic energy.
However, experiments does not support this explanation. Later, in the year of 1905, photoelectric effect has been well explained by Einstein considering light made up of discrete tiny partcles called photons. Each photon has energy E = h, where is the frequency of the incident light. Intensity of light is defined as the number of photons incident on per unit area of the suface per unit time. Hence, increasing light intensity does not increase the energy of each photon. Energy of each photon is dependent only on its frequency . So, kinetic energy of emitted photoelectrons remains constant as long as incident photon frequency is kept constant. This can also be understood from the Einstein famous photoelectric effect equation
From the above equation we can see that for any metal ( is a constant). Hence, kinetic energy of emitted photoelectrons only depent of the frequency of the incident photons and not on the intensity of the incident photon beam.
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