Einstein Explains the Photoelectric Effect
Background
Prior to the Photoelectric Effect experiment all tests indicated that light behaved
like a moving wave. In particular, English physicist Thomas Young’s famous
double-slit experiments showed that light interferes with itself, much like water
waves do. Then Maxwell’s 1864 theory of electromagnetism gave a theoretical
basis for the wave nature of light.
Independently, in 1900 Max Planck made an “inspired guess” to explain
blackbody radiation. He proposed a relationship between energy and
frequency, given in his famous equation:
E=hν
where:
E is energy,
h is Planck’s constant,
which equals 1.05X10-27 grams-centimeters2/second
and ν is frequency
Planck’s mathematics agreed spectacularly with the intensity versus frequency
spectrum measurements from blackbody experiments, but no one knew why.
Did the formula apply to the vibration of atoms? Was it just a mathematical
abstraction? It was an empirical equation in need of a theory.
The Photo-electric Effect
Earlier, in 1887 Heinrich Hertz demonstrated the Photoelectric Effect. He observed that
when light was made to shine on a metal, it leaks electric charge. We now know that
electrons are emitted by the metal when exposed to light. In effect, electrons loosely
bound in atoms are knocked off by the light’s energy. (Figure A-1)
In 1902, Hertz’s assistant, Hungarian-German physicist Philipp von Lénárd’s
Photoelectric Effect tests showed that by increasing the frequency of the light source (a
UV lamp), the electrons fly off the metal with greater energy (i.e. more speed).i In other
words, the frequency of the incoming light somehow affected the energy of the outgoing
electrons. No one had any idea why this was so.

A blackbody is an object which absorbs all the EM radiation it receives. It is also a perfect emitter; it
radiates all this absorbed energy back out (in the infrared for ordinary objects.)
The experiment is summarized as follows (see Fig. A-1):
INPUT
One can vary the input light in two ways:
•
•
Increase or decrease the intensity (brightness) of the light
Increase or decrease the frequency (color) of the light
OUTPUT
The electrons emitted by the metal are measured in two ways:
•
•
The number of electrons emitted (over a given time period)
The speed of the emitted electrons
light
electrons
- - -- - - - - - - -
-
Metal
Figure A-1.The Photoelectric Effect. Shining light on metal dislodges electrons from
atoms in the metal’s surface. The higher the frequency of the incoming light, the greater
the speed of the emitted electrons. The higher the intensity of the incoming light, the
greater the number of electrons dislodged.
So let’s look at the Photo-Electric Effect in more detail, and see how Einstein
solved the riddle it presented.
Increasing the light’s intensity:
What if we increase the intensity of the incoming light? How would this affect
the electrons emitted by the metal?
If light is a wave, then increasing its intensity should increase the height of that
wave. The more intense the beam, the bigger the light beam’s wave. (For
example, the energy in a water wave depends on its height. The bigger the
wave, the more energy it has.)ii Based on this, you would expect that increasing
the intensity of the incoming light would increase its energy.
OK, if this is true, then what would increasing the light’s intensity, hence its
energy do to the emitted electrons? Per Newtonian physics, the speed of the
emitted electrons is directly related to their kinetic energy, KE by:
KE = ½mv2
where
m = mass, and
v = velocity
Based on this logic, you would expect that increasing the intensity of the
incoming light would result in the metal ejecting more energetic electrons; thus
an increase in the speed of the ejected electrons. So you’d expect greater light
intensity in; greater electron speed out.
But this is not at all what happens. The speed of the emitted electrons stays
fixed, no matter how much you increase the incoming light’s intensity. It turns
out the number of electrons ejected increases with an increase in input light
intensity. What actually happens is:
Greater light intensity in; more electrons out (but at the same speed).
Huh? How can this be?
In addition, the Photoelectric Effect experiment shows that you have to increase
the frequency of the light to increase the speed of ejected electrons. In other
words what you see is:
Higher frequency light in; greater electron speed out.
But if light is a wave, what does the frequency of the incoming light have to do
with the speed i.e. the energy of the ejected electrons? This is like saying we
should avoid going into the ocean not when the waves are big, but when they
are higher frequency (more shortly spaced).iii
And to top it off, when the frequency of the light gets low enough, no electrons
are ejected, no matter how intense the light!iv
Summary
Experimental results of the Photoelectric Effect show that:
Increasing or decreasing the intensity of the incoming light:
• Increases or decreases the number of electrons ejected by the
metal, respectively
• But the speed of emitted electrons is unaffected by light
intensity
Increasing or decreasing the frequency of the incoming light:
• Increases or decreases the speed of the ejected electrons,
respectively
At a low enough light frequency
• No electrons are ejects, no matter how much you increase the
intensity of the incoming light!
This was the situation facing physicists in 1905.
Einstein’s Explanation
To resolve this conundrum, Albert Einstein made the bold assertion that light is
made up of particles (later called photons). Einstein proposed that the energy of
these photons of light is given by Planck’s equation:
E=hν
Thus, the greater the frequency of the light, the greater its energy.
Increasing the frequency of the incoming light results in higher energy photons
striking the electrons in the metal. This higher energy is transferred to the
electrons. The electrons are initially held inside atoms by the electromagnetic
force (between the electrons and the protons in the nucleus). The electrons
absorb the photons’ energy, giving them enough energy to escape the nucleus’s
hold. The higher the frequency of the incoming photons; the higher the energy
of the outgoing electrons. Thus the electrons are emitted at greater speed. Voila!
Higher light frequency in means more light energy in; thus more electron
energy, more electron speed out.
And when the frequency of the incoming photons of light is too low, then the
electrons simply don’t absorb enough energy to escape the hold of the atoms. So
no electrons are emitted by the metal at too low a light frequency. Not enough
light energy to knock the electrons off the atoms.
What about intensity? A more intense light beam simply means more photons.
(We now know this is actually an increased probability of finding a photon at a
given location). The higher the intensity of the incoming light, the more photons
there are to be absorbed by the electrons in the metal. Hence, more electrons are
ejected. So increasing the light intensity in increases the number of ejected
electrons out.
Thus Einstein’s explanation agrees with the experimental results in all cases.
Grand Slam Homerun. Pop the Champagne!
But hold your horses; not so fast. Einstein had found a clear, logical explanation
for the results of the Photoelectric Effect. Light behaves like a particle. It is
made of individual packets or quanta of energy; the amount of energy being
proportional to the light’s frequency per Planck’s formula. However, this flew
in the face of all prior experiments which showed that light behaves like a wave.
We now know this wave-particle duality is a property of all matter and energy
(and their antimatter counterparts). Photons, gluons, weak bosons, electrons,
neutrinos, quarks, baryons such as protons and neutrons, mesons, atoms,
molecules, baseballs, people, planets, stars all possess both wave and particle
behavior. However, the waves of everyday (non-microscopic) objects are of
such an ultrahigh frequency that they smear out, so we don’t notice their effects.
Quantum field theory explains that all matter and energy travel like a
(probability) wave but hit (are detected) like a particle. Why this is so remains a
mystery.
Interestingly, there is a practice example of Einstein’s discovery which we use
every time we apply sunscreen lotion. Bernard Schutz points out that sunscreen
lotion acts as a light filter. It prevents light of a wavelength shorter than a
certain UV wavelength from reaching our skin.v Shorter wavelength means
higher frequency, thus higher energy. It is the higher frequency, higher energy
UV photons which cause the damage we call sunburn.
IME
7/4/09
Copyright © Ira Mark Egdall, 2009
For an instructive simulation of the Photo-electric Effect, click on:
http://phet.colorado.edu/web-pages/simulations-base.html
Endnotes
i
M. Fowler, The Photoelectric Effect, see web site at:
http://galileo.phys.virginia.edu/classes/252/photoelectric_effect.html
ii
B. Schutz, Gravity from the Ground Up, p. 86
Ibid
iv
B. Greene, The Elegant Universe, p. 95
v
B. Schutz, Gravity from the Ground Up p. 85
iii