# Development of Quantum Physics III – Finally, the Photoelectric Effect Can be Understood

The third part of this series is about the photoelectric effect.

At first, I’ll try to describe this phenomenon in terms of classical physics, but I’ll fail at it. If we, though, make use of Planck’s quantum hypothesis as explained in the previous article, the discrepancies resulting from the classical viewpoint will resolve and we will gain a deeper understanding of the interaction between radiation and matter.

(You can find the other articles of this series here.)

* * *

# Observations

Heinrich Hertz and Wilhelm Hallwachs did experiments in the late 19th century in which they found that a negatively charged metal plate becomes more and more positive if it’s exposed to ultraviolet light.
You can also put a positively and a negatively charged plate in an air-evacuated glass bulb and apply UV radiation to the negative plate. Then you will notice a change in the potential between them. Hence, some transport of charge must have taken place – namely in form of electrons.
Due to the incoming radiation some electrons are seperated from the negatively charged plate and accelerated towards the positively charged one. (Of course, the electrons break away from the material even if there’s no attracting force of the other plate, but our experimental setup allows relatively easy measurements.)

Knocking electrons out of an atom (graphic)

Experimental setup

# Predictions of the classical point of view

The classical wave model treats electromagnetic radiation (so is light) as waves. The incoming ultraviolet radiation, therefore, consists of waves of the electromagnetic field.
When touching the metal plate, the UV radiation slightly enters the material (about the amount of the radiation’s wavelenght). If the energy of the light beam is bigger than the binding energy of the electrons, they are ripped off of their atomic nuclei and they will leave the metal plate.

What what does “energy of a wave” mean? – That’s quite easy: The bigger the wave’s amplitude the more energetic the wave. (“The higher a water wave the more energy it carries.”) If one increases the light intensity (= amplitude), more electrons will have to be knocked off.
But as a matter of fact, the energy of the wave spreads across many of the material’s electrons.

For instance, consider the following calculation:
Light of a one watt source with a wavelength of 250 nanometeres falls on a zinc plate from one meter distance. The electrons on the zinc plate averagely absorb a power of $2\cdot 10^{-5}~\text{eV}$ per second and per square centimeter. The work necessary for detaching an electron against its binding energy is approximately $4~\text{eV}$ for zinc. We can conclude from that that we would have to wait $2\cdot 10^5$ seconds until electrons start to leave the plate. This amount of time is equivalent to nearly seven work days (assuming a work day of eight hours).

## In a nutshell, the wave model of light makes the following predictions for the outcome of an experiment:

• Increasing the amplitude of the incoming radiation should increase the energy of the electrons.
• It would take two days and seven hours on average until electrons start to break away from the material.

## What tells us an actual experiment?

Lenard performed careful measurements in 1902 and found the following issues:

• The energy of the struck-out electrons only depends on the frequency of the incoming radiation, not on its intensity.
• The bigger the radiation’s intensity the more photoelectrons leave the metal. But these electrons aren’t more energetic.
• Electrons pass out instantly. There was no measurable time delay between the incidence of light and the electron emission.

Oh dear… can theory and experiment be more contradictory? 😉

# Einstein’s courageous hypothesis

In the year 1905, Albert Einstein was able to theoretically explain the above-mentioned experiment employing Max Planck’s quantum hypothesis. Therefore, he received the Nobel Prize in Physics many years later (in 1921).

Albert Einstein, official 1921 Nobel Prize in Physics Photograph

If you don’t think of the incoming radiation as waves, but as a current of small energy packets $h\cdot\nu$ (i. e. quanta) you’ll be able to comprehend the experimental data in a natural and logical way:

The energy $E$ of the incoming quanta is exclusively determined by the frequency $\nu$.
$E=h\cdot\nu$. (For our purposes, the lowercase $h$ is just a small constant called “Planck’s constant”.) The higher the frequency the higher the energy.
If an incoming energy packet (let’s just call it “photon”) doesn’t have enough energy to accelerate an electron against its binding energy, nothing will happen. Equally, nothing will happen, if thousands of these low-energy photons hit the material. But a single photon with higher energy than the binding energy of an electron can strike an electron out of the metal! Raise the number of these high-energy photons (= increase in intensity) and you’ll count more photoelectrons.

Due to this quite plausible and actually simple idea we can explain all of the experiments concerning the photoelectric effect theoretically. Countless experiments confirm the validity of Einstein’s theoretical concept.

We will also apply our successful description of electromagnetic radiation on matter in the next part of the series. You may be curious about the resulting consequences…

__________

 Previous part: The Quantum Hypothesis Next part: How We Found the Wavy Particles