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Author: G. Francesco Tartarelli
E-mail: [email protected]
Movie: 15 minutes in the life of the electron
Movie Clip From 24:23 To 26:35
Director: Luis Mariano Sesé Sánchez, José Antonio Tarazaga Blanco
Film Studio: UNED (Spain)
Scientific level
There are phenomena that are associated to waves like sound waves or waves in
water. Examples are diffraction and interference. When these same phenomena were
observed (and correctly interpreted) also for light, the wave nature of light was
assessed. It was the beginning of the 19th century (thanks to the work of T. Young and
A. Fresnel), even if the wave theory of light had been proposed much earlier (R.
Hooke and C. Huygens, in the 1660s) Light is a peculiar wave. We are used to
associate waves to something which is oscillating: for sound waves what is oscillating
is the medium (air, for example) in which sound is propagating. For light what is
oscillating are electrical and magnetic fields. In fact, light is an electromagnetic wave
(J. C. Maxwell, 1862). If its wavelength is between about 400 and 700 nm we have the
visible light. If the wavelength of the electromagnetic wave is shorter we have
ultraviolet, X and -rays. If it is longer we produce infrared, microwaves and radio
waves. Moreover, light can propagate in vacuum. And its propagation speed in
vacuum, about 300000 km/s, represents the limit speed of nature: nothing can travel
faster than light.
However at the beginning of the 20th century, when studying the interaction of light
with matter, the interpretation of phenomena like light emission from a black body (M.
Planck, 1900), the photoelectric effect (A. Einstein, 1905, described in the
documentary) and later the Compton scattering (A. H. Compton, 1923), forced
scientists to admit that light energy comes in discrete amounts, called light quanta or
photons. In other words a beam of light is a beam of particles called photons: if light
has a frequency , the energy carried by each photon is E=h (where
h=6.6260693x10−34 J s is called Planck constant). This might even appear funny, as in
the beginning scientists (including Newton in the 1660s) thought that light was made
of particles: with this assumption it was straightforward to explain some of the
propagation properties of light, like for example reflection. However, it was not at all
like going back in time. Phenomena like the photoelectric effect and their interpretation
required completely new ideas and set the basis for the development of quantum
physics.
How to reconcile all these observations about the nature of light? Is it wave or it is
particles? We have to accept that it is both. In particular we have to accept that light
propagates like a wave and interacts (exchange energy with something else: for
example when light is emitted or absorbed) like a particle. This is the wave-particle
duality.
This dualism, and in general quantum physics, has been verified by countless
experiments. If you find this hard to swallow and think that you can accept this theory
only because light is such a strange object and because in the end photons, being
massless, are not “real” particles be prepared for more. In 1924 Luis de Broglie
postulated that not only light but everything behaves both as a particle and as a wave.
If an object has momentum p, its wavelength is =h/p where h is again Planck’s
constant. This simple and powerful equation relates the wave and particle properties
of an object. It is clear that, the more massive an object is and the faster it is moving,
the smaller will be its wavelength. Even taking a small object of mass 10 -6 g moving at
10-6 km/h, its wavelength would be about 2.4x10-18 m. This is an extremely small
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wavelength. Indeed to observe a wave phenomenon like diffraction for example, the
wavelength must be comparable to the dimension of the obstacle (a slit, an edge…).
Considering that the diameter of a nucleus is about 10-15 m, it is clear that the wave
properties of such an object cannot be observed. We need smaller objects, like those
one can find inside an atom. In fact, the wave nature of matter undergoes a very
important confirmation when in 1927, in two different experiments, C.J. Davisson and
L.H. Germer at Bell Labs and G.P. Thomson, observed diffraction and interference of
electrons. Electrons constitute, together with protons and neutrons, atoms. They have
a mass of about 9.1x10−31 kg and carry a negative charge of about 1.6x10−19 C. Later
on, wave properties have been measured also for heavier objects like for example
neutrons.
Particle-wave duality does have also practical application as it will be described in the
following example.
How do we “see” things? It works like this. We need to expose an object to a source of
light. If we are outside in the daylight, the light source is provided by the sun for free.
When light hits the atoms the object is made of, various things can happen. The light
can be absorbed, reflected or transmitted by the atoms. The behavior depends on the
nature of the material and on the frequency of the incident light. If some of the light is
reflected or transmitted, it will reach the retina in our eyes which is sensitive to light
and then sent as impulses to our brain. As sunlight is a mixture of various frequencies,
some frequencies will be absorbed while others will be reflected or transmitted by the
object. This is what makes object colored: frequencies that are not absorbed will
determine the color of objects.
If we want to see very small objects or to observe small details of an object we need to
help our eyes with a microscope. An optical microscope is based on the same
principle of the magnifying glass. However, to obtain optimal performances a
microscope uses several lenses and needs a careful design of the light path and good
construction accuracy. The main characteristics of a microscope are its magnifying
power and its resolution. The magnifying power expresses how many times the
dimension of an object appears larger: a very good microscope can exceed a
magnification of 1000x using several tricks. The resolution is the capability of resolving
details in the magnified image. If one keeps magnifying an object, at some point the
image will start loosing details and blur. This is due to the fact the light passing into the
objective aperture is subjected to diffraction (it’s the wave nature of light that enters in
the game here) and so what should appear, for example, like a point object becomes
blurred by a series of interference disks. A criterion (for example, Rayleigh’s criterion)
can be defined to quantify the distance at which two points can still be well separated.
This defines the resolving power of a microscope as d=/2N.A., where  is the light
wavelength used and N.A. is the numerical aperture of the lens system. In air N.A.
cannot exceed 1 (corresponding to a 180o aperture angle of the objective), the
theoretical limit: in practice, N.A. of about 0.95 can be obtained. What about ? From
the formula one can see that the smallest the light wavelength the better resolving
power is achievable. As we already said the visible light has wavelength between 400
and 700 nm. Even taking the smallest side of the spectrum (and assuming that other
factors like lens aberration, illumination quality…are controlled), the resolving power
cannot be better than 200 nm.
As the wavelength of light is the limiting factor it is clear that one can wonder if this
can be reduced. Light with a wavelength of 400 nm is violet light; if we reduce the
wavelength further we have ultraviolet light. Ultraviolet microscopes do exist and use
ultraviolet light to have better resolving power. Quartz optics, for example, has to be
used as glass does not transmit ultraviolet radiation. Moreover as this radiation is
invisible to the human eye, the magnified image has to be made visible via special
techniques like fluorescence, photography and digital image acquisition. Can we go
further down in wavelength? If we do, we enter the X-ray part of the spectrum. One of
the problems here is that it is difficult to provide optics for such a radiation. In a
common microscope light path are created by bending light with lenses using the
phenomenon of refraction. Refraction is the property of light of changing direction
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when going from one medium to another. However, refraction is very small for X-ray
and this complicates things a lot.
The solution to go to shorter wavelength than visible light is to use electron, using their
wave behavior. This brought to the invention of the electron microscope in 1930s. How
does an electron microscope work? First of all if we recall the de Broglie’s relation to
achieve a short electron wavelength we have to give electrons a high momentum. As
electrons are charged particles this can be achieved by accelerating electrons
(emitted by an electron gun) using and electric potential. For a 60 kV potential,
wavelength of 0.005 nm = 5 pm can be reached. To direct and focus the electrons
conventional lenses cannot be used. So one has to use magnetic field to manipulate
the electron beam and let it strike the specimen to be observed. As electrons are
scattered by gas molecules, including air, the electron microscope has to be sealed to
a high vacuum. The beam reaches the specimen and interacts with it. The effects of
these interactions are used to obtain a magnified image of the specimen. The two
main types of electron microscope: the Transmission Electron Microscope (TEM) and
the Scanning Electron Microscope (SEM) make different usage of the electronspecimen interactions. In the TEM, the electrons that pass through the sample are
used to create a magnified image of the specimen. This implies that the specimen has
to be very thin. The magnified image is detected using a specialized device like a
fluorescent screen. The TEM has the better resolving power that can get to about 1
Angstrom (0.1 nm) which is anyway larger than the theoretical value mainly because
of the fact that magnetic fields cannot manipulate electrons as well as modern lenses
can manipulate light. Such resolving power is enough to see up to molecular and even
atomic level. In the SEM microscope, a tightly focused electron beam is used to scan
the specimen in various positions. At each position the electrons that are
backscattered from the surface of the samples or that are emitted as secondary
electrons are collected and counted. Mapping this signal with the beam position, the
magnified image of the specimen can be built on a screen. SEM microscopes have a
resolution which is worse than TEM microscope: however they have the advantage
that the specimen does not need to be thin and that the reconstructed image has 3D
information (while TEM images are 2D).
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