Physics

Einstein's interpretation for the photoelectric effect


In 1905, Einstein proposed a new theory for light, using the photoelectric effect to prove whether his ideas were indeed correct.

Initially, Planck had restricted the concept of energy quantization to only the electrons in the walls of a blackbody. To him, as he radiated energy, it spread through space, just as waves spread in water. Einstein, in turn, proposed that energy would be quantified in concentrated packages that would later be called photons.

Einstein focused his attention on the corpuscular form in which light is emitted and absorbed, not on the wave form as it propagates. He argued that Planck's requirement that the energy of the electromagnetic waves emitted by a source be a multiple of hf implied that by going from an nhf energy state to a state whose energy was (n-1) hf, the source would emit a discrete pulse of electromagnetic radiation with hf.

It initially assumed that this energy package would be located in a small volume of space and would remain located there as it moved away from the source at speed c, the speed of light.

The energy E of the package, or rather of the photon, is related to the frequency f according to the equation:

In the photoelectric effect, a photon is completely absorbed by an electron in the photocathode. Thus, when emitted from the metal surface, the electron kinetic energy will be given by:

Where:

hf = incident absorbed photon energy;

w = work required to remove electron from metal.

Some electrons are more strongly bonded than others, so that in the case of the weakest bond and no internal loss, the photoelectron will emerge with maximum kinetic energy, Kmax. Like this:

Where w0, a characteristic energy of the metal, called the work function, is the minimum energy required for an electron to cross the metal surface and escape the attractive forces that attach it to the metal.

Since Kmax= eV0, we can rewrite the photoelectric effect equation as:

The objection that Kmax Depending on the intensity of the illumination, the photon theory fully agrees with the results obtained experimentally: doubling the light intensity simply doubles the number of photons and hence doubles the intensity of the electric current, but this does not change the hf energy of each photon. .

As for the existence of a frequency threshold, this idea is easily eliminated when the maximum kinetic energy is zero:

This means that a photon of frequency f0 It has exactly the energy needed to eject photoelectrons and thus no excess kinetic energy.

The absence of delay is explained by the fact that the required power is supplied in concentrated packages. Thus, contrary to popular belief, it is not evenly spread over a large area, since if there is light shining on the cathode, there will be at least one photon to hit it, which will be instantly absorbed by some atom. and will cause the immediate emission of a photon.

Finally, Einstein's model states that a photon of frequency f has exactly the energy hf, not multiples of hf. However, it is evident that if we are dealing with n photons with frequency f, the energy at that frequency will be nhf.