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The Photoelectric Effect

Introduction The
Quantum Theory was the second of two theories
which drastically changed the way we look at our
physical world today, the first being Einsteins
Theory of Relativity. Although both theories
revolutionized the world of physics, the Quantum
Theory required a period of over three decades to
develop, while the Special Theory of Relativity
was created in a single year. The development of
the Quantum Theory began in 1887 when a
German physicist, Heinrich Hertz, was testing
Maxwells Theory of Electromagnetic Waves.

Hertz discovered that ultraviolet light discharged
certain electrically charged metallic plates, a
phenomenon that could not be explained by
Maxwells Wave Theory. In order to explain this
phenomenon termed the photoelectric effect,
because both light and electricity are involved, the
Quantum Theory was developed. The
Photoelectric Effect Maxwells work with the
Theory of Electromagnetic Waves may seem to
have solved the problem concerning the nature of
light, but at least one major problem remained.

There was one experiment conducted by Hertz,
the photoelectric effect, which could not be
explained by considering light to be a wave. Hertz
observed that when certain metals are illuminated
by light or other electromagnetic radiation, they
lose electrons. Suppose we set up an electric
circuit. In this circuit the negative terminal of a
battery has been connected to a piece of sodium
metal. The positive terminal of the battery is
connected through a meter that measures electric
current, and to another piece of metal. Both of
these metal plates are enclosed in a sealed glass
tube in which there is a vacuum. When there is no
light illuminating the sodium plate, no current will
flow, and therefore there is no reading on the
meter. A reading on the meter will only occur
when electrons are liberated from the metal
creating a flow of electric current. However, if the
sodium plate is exposed to light, an electric current
will flow and this will register on the meter. By
blocking the light from illuminating the sodium
plate, the current will then stop. When the amount
of light striking the plate is increased, the amount
of current also increases. If various colours of light
are tested on the sodium plate it will be discovered
that violet and blue light causes current flow.

However, colours of light toward the other end of
the spectrum (red) do not result in a flow of
electric current when they illuminate the sodium
plate. The electrons will only be emitted if the
frequency of the radiation is above a certain
minimum value, called the threshold frequency
(fo). The threshold frequency varies with each
metal. When the sodium plate was exposed to
high frequency light, electrons were emitted and
were attracted to the positive terminal, causing a
flow of current. However, when a low frequency
light was used no electrons were emitted and
therefore there was no current. Observations of
the Photoelectric Effect 1. Current flows as soon
as the negative terminal is illuminated. 2. High
frequency light causes electrons to be emitted from
the sodium, however, a lower frequency light does
not. 3. The energy of the emitted electrons does
not depend upon the intensity (brightness) of the
light, it is dependent on the frequency of the light.

A higher frequency of light causes higher energy
electrons. 4. The amount of current that flows is
dependent upon the intensity (brightness) of the
light. Prior to the 1900s light was considered to
be wave-like in nature. This was due to the
success of Maxwells Electromagnetic Theory.

However, much of the phenomenon observed
during the photoelectric effect was in contradiction
to the Wave Theory of Light. For instance, the
energy contained in electromagnetic waves, and
the amount of energy that would strike a sodium
electron can be calculated. Such a calculation
shows that an electron could indeed gain enough
energy to be liberated from the sodium, but only
after the sodium had been illuminated for several
hours. However, this was not the case for
photoelectricity, in which the electrons are freed
instantly. The Electromagnetic Theory sustains that
light waves carry energy whether they are of high
or low frequency. Therefore, the frequency of light
should not be a factor in the emitting of electrons.

Once, again the photoelectric effect contradicts
the Wave Theory. In the photoelectric effect only
high frequency light can cause electrons to be
emitted no matter how long the light is shined. The
photoelectric effect was a major roadblock in the
way of total acceptance of the Wave Theory of
Light. Einsteins Theory In 1905, Albert Einstein
published a revolutionary theory that explained the
photoelectric effect. According to Einstein, light
and other forms of radiation consist of discrete
bundles of energy which were later given the term
photons. The energy contained in each photon
depends on the frequency of the light in which they
are found. The energy of the emitted
photoelectron can be determined using the
equation E = hf, where h is Planks constant,
6.626 x 10 34 J/Hz. According to Einsteins
theory an electron is ejected from the metal by a
collision with a single photon in the process, all the
photon energy is transferred to the electron and
the photon ceases to exist. However, the result is
the creation of a photoelectron. Since electrons
are held together in a metal by attractive forces,
some minimum energy Wo (work function) is
required to release an electron from the binding
force. If the frequency (f) of the incoming light
causes hf to be less than Wo, then the photons will
not have enough energy to emit any electrons.

However, if hf is greater than Wo, then the
electrons will be liberated and the excess energy
becomes the kinetic energy of the photoelectron,
allowing it to travel, creating an electric current.

Einsteins theory uses the existence of a threshold
frequency to explain the photoelectric effect. A
photon with minimum energy hf is required to emit
an electron from the metal. Light with a frequency
greater than the threshold frequency (fo) has more
energy than required to emit an electron. The
excess energy again becomes the kinetic energy of
the electron, thus, Ek = hf – hfo. This equation is
known as Einsteins Photoelectric Equation. An
electron cannot accumulate photons until it has
enough energy to break free; only one photon can
interacts with one electron at a time. In Einsteins
equation hfo, is actually the minimum energy
required to free an electron. Not all electrons in a
solid have the same energy; most need more then
the minimum (hfo) to escape. Therefore, the
kinetic energy of the emitted electrons is actually
the maximum kinetic energy an emitted electron
could have. Einsteins theory can be tested by
indirectly measuring the kinetic energy of the
emitted electrons. A variable electric potential
difference across the tube makes the anode
negative. Since, the anode rejects the emitted
electrons from the cathode, the electrons must
have sufficient kinetic energy at the cathode to
reach the anode before turning back. A light of
measurable frequency f, is directed at the cathode.

An ammeter measures the current flowing through
the circuit. As the opposing potential difference is
increased, the anode is made increasingly more
negative. At some voltage, called the stopping
potential, there is a zero reading from the ammeter
because the electrons do not reach the anode.

This is due to an insufficient amount of supplied
energy to the electrons. The maximum kinetic
energy of the electrons at the cathode equals their
potential energy at the anode. Emax = -qVo,
where Vo is the magnitude of the stopping
potential in volts (J/C), and q is the charge of the
electron (-1.60 x 10-19C). The joule is too large
a unit of energy to use with atomic systems,
therefore the electron volt (eV) is used instead. 1
eV = (1.60 x 10-19C) (1V) = (1.60 x 10-19C)
(V). Also, 1 eV = 1.60 x 10-19J. The results from
this experiment will show that higher frequency
radiation will have higher stopping potentials, and
lower frequency radiation will have lower stopping
potentials, holding true to Einstein’s hypothesis.

Conclusion The photoelectric effect revolutionized
the way the nature and behaviour of light is
understood. It also saw the dawn of modern
physics with the use of the Particle Theory, and it
catapulted Einstein to Nobel Prize-winning status.

Today, the phenomenon has many practical
applications such as alarm systems that activate
when the flow of light is interrupted.

Photoelectricity also helps explain the physics of
photosynthesis, by which plants make their own
food. It’s truly evident that the photoelectric effect
and its explanation played an important historical
role in science.
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