Transcript Slide 1

Photoelectric effect and the dual
nature of light
As we said before, the 1805 double-slit experiments in
which Thomas Young observed distinct interference
effects wielded a “mortal blow” to Newton’s theory that
described light as a stream of tiny ‘light particles”.
The following years were marked by many new triumphs
of the wave theory of light. A real milestone event was
the theory of James C. Maxwell (1861-62) that led to
the prediction that light is an electromagnetic wave.
But still missing was an experimental proof that
EM waves can be generated by electric circuits,
as was also predicted by the Maxwell theory.
A series of crucial experiments that
validated Maxwell’s theory was carried
out by a German physicist Heinrich
Hertz in 1887. His results were accepted as the final proof for the electromagnetic nature of light waves.
But Mother Nature is mischievous…
Heinrich Hertz
(1857-1894)
Because in the very same year of 1887, the very
same person, Hertz, discovered another surprising
effect induced by light: namely, that light incident
on metal surfaces knocks out negative electric
charge from them! This phenomenon was named
the Photoelectric Effect.
In 1887 it was not known that the carriers
of negative charge are tiny particles – the
electrons. They were discovered only ten
years later, in 1897, by a famous British
physicist, J.J. Thomson (who is perhaps
better known as Lord Kelvin).
J. J. Thomson
(Lord Kelvin)
Soon it was understood and confirmed
by new experiments
that in the photoelectric effect light knocks
out electrons from the
metal.
Was it a simple explanation? Not really… It caused
a lot of embarrassment among physicists because…
the experimental findings seemed to be in clear
contradiction with the wave nature of light!
It’s natural to expect that it is the electric field of the EM wave
that rips out the electrons from the metal.
Light of lower frequency (red):
Light of higher frequency (blue):
Lower light
Intensity:
Higher light
Intensity:
The maximum electric field value depends on
the intensity, but not on the frequency.
So, what can be expected? – and how do the
expectations agree with the observations?
1. Expected, based on the wave theory:
Increasing light intensity  increasing kinetic
energy of the electrons knocked out.
Observed: Increasing the intensity of the light
increases the number of photoelectrons, but
not their maximum kinetic energy!
2. Wave theory, expected: it’s the electric field
of the EM wave that “pulls out” the electrons
from the metal. The strength of the wave’s
electric field depends on it’s intensity, but not
frequency. Then, lights of all colors should
produce similar effects.
Observed: Red light does not cause
the ejection of electrons, no matter
what the intensity!
Observed: Green light does eject electrons,
but their kinetic energy….
…is lower than of those ejected by violet
light!
Let’s summarize, in a graphic form:
At the beginning of the XX century, the peculiar
behavior of photoelectrons was thought of as
one of the “major unsolved mysteries” in physics.
It was young Albert Einstein
who found a solution of this
riddle. In 1905, he showed
that one can fully explain the
photoelectric effect by assuming that light is actually made
up of lots of small “packets”
of energy called photons that
behave like particles.
According to Einstein, the energy carried by
an individual photon depends only on its
frequency ν – namely, as:
E photon  h 
where h  6 . 626  10  34 J  s is a constant known
as the “Planck Constant”.
In the photoelectric effect, the photon disappears, and all its energy acquired by the photoelectron in the form of kinetic energy K :
K photoelect
ron
in the metal
 h 
It already explains two facts:
1. Light intensity increases  number of photons
increases  number of photoelectrons increases (but not their kinetic energy!).
2. Light frequency increases  photon energy
increases  photoelectron energy increases.
Still, it does not answer the
question why red light does
not produce photoelectrons!
In order to explain the latter fact, we need to say
something about electrons in metals:
They can be thought of as sort of an “electron fluid”
(actually, the official term is “Fermi fluid of mobile
electrons”).
There is much analogy
between this fluid, and
water in a glass not
filled up to the rim.
The potential energy of
the “topmost” electrons
is lower than that of
electrons outside (i.e.,
of free electrons) by W .
Therefore, a portion of
energy equal W is needed to pull the electron out of the metal.
By tradition, W is called
the “Work Function”
In view of the above, taking into account the
energy conservation, we can conclude that
the kinetic energy of a photoelectron getting
out of the metal is:
K photoelect
ron
 h
  W

photon
energy
work
function
This is the famous Einstein’s formula, for which
he was awarded a Nobel Prize in 1921
Small digression: energy units
The energy unit in the SI system is a Joule (J):
1J 1
kg  m
s
2
2
However, the energies of photons expressed in
Joules would be very small numbers. Therefore,
for the sake of convenience, we use a much
smaller unit called “electron-Volt” (eV):
1 eV  1.602  10
-19
J
Digression (2): Planck Constant in terms of eV:
h  4 . 136  10
 15
eV  s
The photon energy is E=hν . But the frequency ν
of visible light is a very large number, which also
makes it inconvenient; a more “user-friendly” is
the wavelength  :
E photon  h   h

1240 eV  10

c

9
m

4 . 136  10

 15
eV  s  3  10 m/s
8

1240 eV  nm

Digression (3): Examples:
E photon 
1240
 in nm

eV
 [nm]
Eph [eV]
700
1.77
550
2.25
400
3.10
Back to photoelectric effect:
K electr.  E ph.  W
Example: PE in Potassium metal:
Potassium: W = 2.0 eV
Here is another
instructive picture
(Tmax in this graph
has the same
meaning as K in
the other slides,
and V(z) is the
potential energy).
The values of work function W
for various metals (note that
Cesium (Cs) has a record-low
work function value).
In 1905, Einstein’s theory of PE based on “light
particles” (photons) was so revolutionary that
it was met with wide scepticism. However, in
the following years much new experimental
evidence supporting the theory was obtained,
and the scepticism gradually changed to a
wide acceptance.
Did Einstein’s theory “wipe out” the wave theory?
No, the wave theory is still in good health! How
comes? Well, we have to accept that light has a
“dual nature”: in some phenomena it behaves
like a wave, and in some others, like a beam of
particles.
Discussion of the dual nature of light in greater
detail goes beyond the scope of this course –
however, I encourage all of you to learn more
for your own “intellectual profit”. There is a lot
of material on this subject on the Web.
PRACTICAL EXAMPLE:
In an experiment with a metal sample, it was found
that light of wavelength 420 nm ejects photoelectrons
of energy 0.65 eV from its surface, and light of wavelength 310 nm ejects electrons of energy 1.69 eV.
Find the value of the work function of this metal –
show that you don’t need to know the Planck
constant value to solve the problem.