### Heinz Heinzmann

# Photoelectric Effect

## Wave or Particle?

In 1905 Einstein explained
the photoelectric effect with the assumption that the energy of the radiation
field is quantized.

The experimental facts of the photoelectric effect:

If a metal
plate gets irradiated by UV-light with a frequency *ν* above
a certain limit *ν*_{0}
, electrons are set free without any delay. The
kinetic energy of these electrons depends only on the frequency
*ν* of the radiation.

This is in
blatant conflict with the wave model of the light, according to which the
displacement of electrons should take place at any light frequency and their
energy should have to be dependent on the intensity of the light. Furthermore,
an enormous delay (under realistic conditions thousands of hours) until the
displacement of the first electron would have to be expected.

As is well known Einstein’s solution was to assume an interaction between light and matter in form
of an *impact process* of particles, i.e. of a light-quant with the energy h*ν*
and an electron bound with the energy A. Then from the energy balance the following relation
results:

h*ν* =
A + mv^{2}/2
(A … displacement work)

Let us first ask which concrete model assumptions lead to the contradiction to the wave model of
the light.

The answer is straightforward: The contradiction follows from the simple assumption that the
interaction between light and electrons takes place according to the paradigm
of macroscopic, “mechanical” interactions – not different from e.g. water waves
and pebbles. Would this be the case, then as a matter of fact it would have to
be expected that the kinetic energy of the electrons depends on the
intensity of the light. (Thus it is the origin of physics from mechanics, which
leads to these contradictory model assumptions).

However we now show:

**If ***both*,
light and electron are understood as waves then we obtain the same result
already under the simplest model assumptions.