Not only did Compton’s work explain the reduction in frequency, but his analysis of the collision also correctly relates the direction of the
scattered x-rays to their change in frequency. When a moving particle strikes a stationary target, its change in momentum and the angle at
which it scatters are related. Consider the photon-electron collision. If the direction at which the photon comes out is virtually unchanged from
its original direction, then its change in momentum is small, and very little momentum (and energy) will be given to the electron. In other words,
the two particles just suffered a glancing blow.
When Compton observed x-ray photons whose direction was barely changed, he saw that their frequency was also practically unchanged.
Again, the basics of collisions held true.
As the angle between the emitted and incident radiation increased, the change in momentum increased. More momentum (and energy) is
transferred to the electron. Radiation that was backward scattered suffered the largest reduction in frequency.
Compton’s work with x-rays confirmed that electromagnetic radiation possesses momentum, a property that had been classically associated
with particles. It was increasingly hard to argue that light should only be considered a wave when it could be demonstrated that it had
momentum, and its interaction with matter could be modeled using a classical explanation of collisions. It became necessary to admit that
under certain conditions the wave nature of light is observed while in different experiments the particle nature is needed to explain the results.
37.2 - Matter waves
After Compton’s observations, physicists were forced to confront the fact that light,
which had been thought of as solely an electromagnetic wave, also has properties of a
particle. This new viewpoint enabled them to understand the experimental data they
were confronting.
However, there still remained many enigmas. For instance, Bohr had constructed his
model of the hydrogen atom, which successfully predicted observed emission and
absorption spectra. Bohr proposed quantized energy states for the electron, starting
with a classical view of the electron as a negatively charged, point-sized particle circling
the positive nucleus, and using Planck's work. However, Bohr was not able to
demonstrate why his model was correct.
In 1923, a French doctoral student named Louis de Broglie proposed a simple idea to
help to rescue the physicists from their intellectual tar pit. Recognizing that light has
both wave and particle properties, he reasoned that nature is symmetrical, and that the
same is true for matter. De Broglie asserted that particles such as electrons have both
particle and wave properties.
To quote de Broglie: “...I had a sudden inspiration. Einstein’s wave-particle dualism was
an absolutely general phenomenon extending to all physical nature...”
Although it was a simple idea, it propelled the next revolution in physics.
De Broglie conceived of the electron in an atom as a standing “matter wave” vibrating
around the nucleus. In other words, the electron is “smeared out” instead of being a
single point-sized particle. Let’s consider the implications of representing an electron
with such a wave, as shown in Concept 2.
As you may recall, a standing wave results from waves that interfere with one another.
For there to be constructive interference, peak must meet peak, and trough must meet
trough. In contrast, if at a given location, the peak of one wave meets the trough of
another, the result is destructive interference í a flat line, in essence.
Here, the string is looped into a circle, and the length of the string is the circumference
of the circle. A wave begins its circular path around the string, and when it makes a
loop, it meets up with itself.
If as it makes a second journey around, peak meets peak, the result will be a standing
wave. On the other hand, if peak meets trough, the wave will cancel. The relationship
between the circumference of the circle and the wavelength determines whether there
is constructive interference. In Concept 2, we show an example where there is
constructive interference.
The wave shown to the right does not represent the actual path of the electron through
space. It is a matter wave í a way to visualize the likelihood of finding the electron at a
given location. If the amplitude of the wave is zero, then the likelihood is zero, and there
will be no electron.
This provides one piece of the puzzle. Only certain wavelengths are possible for a given
orbit, but that doesn’t prevent any orbit being possible í it just dictates possible
wavelengths.
The other piece of the puzzle comes from considering the angular momentum of the
electron. De Broglie showed why Bohr’s quantization argument could be justified by
considering the angular momentum of the electron and the relationship between
momentum and wavelength.
To quantify the wavelength of a matter particle such as an electron, de Broglie proposed that the same equation that describes the momentum
De Broglie
Matter is particle with wave-like
properties
De Broglie and the electron
orbits
Wave-like properties explain quantized
orbits
Wavelength of a matter particle
Ȝ = wavelength
p = momentum
h = Planck’s constant, 6.63×10í^34 J·s
(^690) Copyright 2000-2007 Kinetic Books Co. Chapter 37