Question

How did Einstein’s photoelectric effect prove that light has a wave-particle duality?

Answer 1

Answer: There are many things needed to be pointed out. First of all, Einstein was not the first one to observe the photoelectric effect, there were Hallwachs and Thompson and his archrival Phillip Lenard before him. Einstein even credited Lenard for his observations in Annus Mirabilis.

He did explain the observations though considering the particle nature and his explanations only established the particle nature. Wave particle duality was a combined effect of Einstein's particle and Thomas young's wave model ( we shouldn't forget other geniuses' contribution like Huyghen, Fresnel, fraunhoffer, hallwachs, planck, wien, Thompson etc.).

He achieved it via a derivation using Wien's law showing that light behaves as number of balls where number of balls are given by [Total Energy of the light / h]. Therefore establishing that light is in fact a stream of particles called photons each having energy h.

Coming to the real answer and explanation of photoelectric effect using his newly derived result which was impossible to explain using young's wave model of light!

Three brilliant challenges with wave model were beautifully solved with particle one as:

1) Kinetic energy of the ejected electrons depended on the frequency (direct relation) and not on the intensity which should have been the case had light behaved as wave! Thus showing E=h for one photon, i.e. more energetic the hitting photon, more KE the electron has.

2) Time lag between hit & eject should have been high for weak sources of light going to even minute long according to wave theory (the calculation is logical and simple), but experiments showed as hasty as 10^-9 secs, thus implying that energy gets transferred in one go as is classically done by balls colliding.

3) Existence of cutoff frequency of light for electron emission and that too with high intensities was a big blow to wave model. With wave model, high intensities of light should have meant high energy transfer and emissions. But particle model ruled out this by showing if frequency of light is below a cutoff (h<E_req), no emission will take place.

A sensible realisation of points above and wave model clears the picture that the coin of light is wave while travelling and particle while hitting!

In photoelectric effect we perceive light as photons associated with a particular frequency.

In waves, it can be observed behaving as a wave of a given wavelength making beautiful interference and diffraction patterns!

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