why wave theory failed to explain photoelectric effect?

Photo electric effect is the removal of electron on incident of electromagnetic radiation on metal surface. But scientist of the 20th century were not able to explain this by the then existent wave theory of light. But why?. To understand the problem with wave theory we need to understand few points:

1) the energy/intensity of a wave is directly proportional to square of amplitude

2) Amplitude is the max displacement from the mean position

    Now if we have to analyze photoelectric effect through wave theory then we can conclude two things

1) The increase in intensity at constant frequency (increase in amplitude) will result in more energetic electrons.

2) The increase in frequency will result in ejection of more electrons

These two results seems convincingly right according to wave theory but when experiments were conducted the results were exact opposite. the observations were:

1) the increase in intensity at constant frequency resulted in ejection of more electrons at same energy

2) the increase in frequency resulted in the release of same number of electrons at higher energy 

Planck proposed that light also has particle nature and energy is transferred in discrete packets called photons. The energy of photons is proportional to frequency

Using this Einstein was able to explain photoelectric effect

THANKS FOR READING !!

-Arvin Gupta