What else did Einstein do to photons? Let us hear from
Michael Fowler. Fowler is a very witty and to-the-point speaker.
He used to be and perhaps still is very proud of his English origin.
I once asked him whether he could name a good king or queen after
Queen Elizabeth I. His answer was Yes. Winston Churchill. You will
enjoy his writings on modern physics. YSK (2004.12.12)
Michael Fowler
The most dramatic prediction of Maxwell's theory of electromagnetism,
published in 1865, was the existence of electromagnetic waves moving at the
speed of light, and the conclusion that light itself was just such a wave. This
challenged experimentalists to generate and detect electromagnetic radiation
using some form of electrical apparatus. The first clearly successful attempt
was by Heinrich Hertz in 1886. He used a high voltage induction coil to cause a
spark discharge between two pieces of brass, to quote him, "Imagine a
cylindrical brass body, 3 cm in diameter and 26 cm long, interrupted midway
along its length by a spark gap whose poles on either side are formed by spheres
of 2 cm radius." The idea was that once a spark formed a conducting path
between the two brass conductors, charge would rapidly oscillate back and forth,
emitting electromagnetic radiation of a wavelength similar to the size of the
conductors themselves. To prove there really was radiation emitted, it had to be detected. Hertz
used a piece of copper wire 1 mm thick bent into a circle of diameter 7.5 cms,
with a small brass sphere on one end, and the other end of the wire was pointed,
with the point near the sphere. He added a screw mechanism so that the point
could be moved very close to the sphere in a controlled fashion. This "receiver"
was designed so that current oscillating back and forth in the wire would have a
natural period close to that of the "transmitter" described above. The presence
of oscillating charge in the receiver would be signaled by a spark across the
(tiny) gap between the point and the sphere (typically, this gap was hundredths
of a millimeter). (It was suggested to Hertz that this spark gap could be
replaced as a detector by a suitably prepared frog's leg, but that apparently
didn't work.) The experiment was very successful - Hertz was able to detect the radiation
up to fifty feet away, and in a series of ingenious experiments established that
the radiation was reflected and refracted as expected, and that it was
polarized. The main problem - the limiting factor in detection -- was being able
to see the tiny spark in the receiver. In trying to improve the spark's
visibility, he came upon something very mysterious. To quote from Hertz again
(he called the transmitter spark A, the receiver B): "I
occasionally enclosed the spark B in a dark case so as to more easily make the
observations; and in so doing I observed that the maximum spark-length became
decidedly smaller in the case than it was before. On removing in succession the
various parts of the case, it was seen that the only portion of it which
exercised this prejudicial effect was that which screened the spark B from the
spark A. The partition on that side exhibited this effect, not only when it was
in the immediate neighbourhood of the spark B, but also when it was interposed
at greater distances from B between A and B. A phenomenon so remarkable called
for closer investigation." Hertz then embarked on a very thorough investigation. He found that the small
receiver spark was more vigorous if it was exposed to ultraviolet light from the
transmitter spark. It took a long time to figure this out - he first checked for
some kind of electromagnetic effect, but found a sheet of glass effectively
shielded the spark. He then found a slab of quartz did not shield the spark,
whereupon he used a quartz prism to break up the light from the big spark into
its components, and discovered that the wavelength which made the little spark
more powerful was beyond the visible, in the ultraviolet. In 1887, Hertz concluded what must have been months of investigation: "… I
confine myself at present to communicating the results obtained, without
attempting any theory respecting the manner in which the observed phenomena are
brought about." The next year, 1888, another German physicist, Wilhelm Hallwachs, in Dresden,
wrote: "In a recent publication Hertz has described investigations on the
dependence of the maximum length of an induction spark on the radiation received
by it from another induction spark. He proved that the phenomenon observed is an
action of the ultraviolet light. No further light on the nature of the
phenomenon could be obtained, because of the complicated conditions of the
research in which it appeared. I have endeavored to obtain related phenomena
which would occur under simpler conditions, in order to make the explanation of
the phenomena easier. Success was obtained by investigating the action of the
electric light on electrically charged bodies." He then describes his very simple experiment: a clean circular plate of zinc
was mounted on an insulating stand and attached by a wire to a gold leaf
electroscope, which was then charged negatively. The electroscope lost its
charge very slowly. However, if the zinc plate was exposed to ultraviolet light
from an arc lamp, or from burning magnesium, charge leaked away quickly. If the
plate was positively charged, there was no fast charge leakage. (We showed this
as a lecture demo, using a UV lamp as source.) Questions for the reader: Could it be that the ultraviolet light
somehow spoiled the insulating properties of the stand the zinc plate was on?
Could it be that electric or magnetic effects from the large current in the arc
lamp somehow caused the charge leakage? Although Hallwach's experiment certainly clarified the situation, he did not
offer any theory of what was going on. In fact, the situation remained unclear until 1899, when Thomson established
that the ultraviolet light caused electrons to be emitted, the same
particles found in cathode rays. His method was to enclose the metallic surface
to be exposed to radiation in a vacuum tube, in other words to make it the
cathode in a cathode ray tube. The new feature was that electrons were to be
ejected from the cathode by the radiation, rather than by the strong electric
field used previously. By this time, there was a plausible picture of what was going on. Atoms in
the cathode contained electrons, which were shaken and caused to vibrate by the
oscillating electric field of the incident radiation. Eventually some of them
would be shaken loose, and would be ejected from the cathode. It is worthwhile
considering carefully how the number and speed of electrons
emitted would be expected to vary with the intensity and color of
the incident radiation. Increasing the intensity of radiation would shake the
electrons more violently, so one would expect more to be emitted, and they would
shoot out at greater speed, on average. Increasing the frequency of the
radiation would shake the electrons faster, so might cause the electrons to come
out faster. For very dim light, it would take some time for an electron to work
up to a sufficient amplitude of vibration to shake loose. In 1902, Lenard studied
how the energy of the emitted photoelectrons varied with the intensity of the
light. He used a carbon arc light, and could increase the intensity a
thousand-fold. The ejected electrons hit another metal plate, the collector,
which was connected to the cathode by a wire with a sensitive ammeter, to
measure the current produced by the illumination. To measure the energy of the
ejected electrons, Lenard charged the collector plate negatively, to repel the
electrons coming towards it. Thus, only electrons ejected with enough kinetic
energy to get up this potential hill would contribute to the current. Lenard
discovered that there was a well defined minimum voltage that stopped any
electrons getting through, we'll call it Vstop. To his
surprise, he found that Vstop did not depend at all on the
intensity of the light! Doubling the light intensity doubled the number
of electrons emitted, but did not affect the energies of the emitted
electrons. The more powerful oscillating field ejected more electrons, but the
maximum individual energy of the ejected electrons was the same as for the
weaker field. But Lenard did something else. With his very powerful arc lamp, there was
sufficient intensity to separate out the colors and check the photoelectric
effect using light of different colors. He found that the maximum energy of the
ejected electrons did depend on the color --- the shorter wavelength,
higher frequency light caused electrons to be ejected with more energy. This
was, however, a fairly qualitative conclusion --- the energy measurements were
not very reproducible, because they were extremely sensitive to the condition of
the surface, in particular its state of partial oxidation. In the best vacua
available at that time, significant oxidation of a fresh surface took place in
tens of minutes. (The details of the surface are crucial because the fastest
electrons emitted are those from right at the surface, and their binding to the
solid depends strongly on the nature of the surface --- is it pure metal or a
mixture of metal and oxygen atoms?)
The energy-momentum relation for massless particles is E = cp.
This expression is quite different from E = p2/2m .
It is very difficult to reconcile this difference without Einstein's
E = [(mc2)2 + (cp)2]1/2,
which he invented in 1905.
The Photoelectric Effect
University of Virginia
Physics 252 Home
Page
Link
to Previous LectureHertz Finds Maxwell's Waves: and Something Else
Hallwachs' Simpler Approach
J.J. Thomson Identifies the Particles
Lenard Finds Some Surprises
Question: In the above figure, the battery represents the potential Lenard used to charge the collector plate negatively, which would actually be a variable voltage source. Since the electrons ejected by the blue light are getting to the collector plate, evidently the potential supplied by the battery is less than Vstop for blue light. Show with an arrow on the wire the direction of the electric current in the wire.
Einstein Suggests an Explanation
In 1905 Einstein gave a very simple interpretation of Lenard's results. He
just assumed that the incoming radiation should be thought of as quanta of
frequency hf, with f the frequency. In photoemission, one such
quantum is absorbed by one electron. If the electron is some distance into the
material of the cathode, some energy will be lost as it moves towards the
surface. There will always be some electrostatic cost as the electron leaves the
surface, this is usually called the work function, W. The most energetic
electrons emitted will be those very close to the surface, and they will leave
the cathode with kinetic energy
E = hf - W.
On cranking up the negative voltage on the collector plate until the current
just stops, that is, to Vstop, the highest kinetic energy
electrons must have had energy eVstop on leaving the cathode.
Thus,
eVstop = hf - W
Thus Einstein's theory makes a very definite quantitative prediction: if the
frequency of the incident light is varied, and Vstop plotted
as a function of frequency, the slope of the line should be h/e.
It is also clear that there is a minimum light frequency for a given metal, that for which the quantum of energy is equal to the work function. Light below that frequency , no matter how bright, will not cause photoemission.
Millikan's Attempts to Disprove Einstein's Theory
If we accept Einstein's theory, then, this is a completely different way to
measure Planck's constant. The American experimental physicist Robert
Millikan, who did not accept Einstein's theory, which he saw as an attack on
the wave theory of light, worked for ten years, until 1916, on the photoelectric
effect. He even devised techniques for scraping clean the metal surfaces inside
the vacuum tube. For all his efforts he found disappointing results: he
confirmed Einstein's theory, measuring Planck's constant to within 0.5% by this
method. One consolation was that he did get a Nobel prize for this series of
experiments.
References
'Subtle is the Lord...' The Science and Life of Albert Einstein, Abraham Pais, Oxford 1982.
Inward Bound, Abraham Pais, Oxford, 1986
The Project Physics Course, Text, Holt, Rinehart, Winston, 1970
Physics 252
Home Page
Link
to Next Lecture
Copyright ©1997 Michael Fowler