Quantum Theory of Light.

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Lecture 15

• Quantum Theory of Light.
• Matter Waves.

• Photoelectric effect
• Photons
• De Broglie Waves
• Uncertainty Principle

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Modern and Classical Physics
Classical physics treats particles and waves as
different aspects of the reality.
However, the physical reality arises from
small-scale world of atoms and molecules,
electrons and nuclei.
Electrons behave as particles because they have
charge and mass, but moving electrons also show
evidence of behaving as waves (diffraction,
interference).
The wave-particle duality is central to an
understanding of modern physics.
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Photoelectric Effect

• Experiments showed that light directed onto a
  metal surface causes the surface to emit
  electrons.
• This phenomenon is called photoelectric effect.

• 3 features of photoelectric effect
• The electron is always emitted at once even under
  a faint light.
• A bright light causes more electrons to be
  emitted than the faint light, but the average
  kinetic energy of the electrons is the same.
• The higher the light frequency, the more kinetic
  energy the electrons have.

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Photons
The electromagnetic theory of light could not
explain the experimental results concerning
photoelectric effect.
In 1905 Albert Einstein created the quantum
theory of light.
Einstein proposed that light consists of small
separate bursts of energy called photons.
In 1900 Max Planck proposed that hot objects
contribute energy in separate units, called
quanta, to the light they produce.
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Photons
E h f E quantum energy, f frequency, h
Plancks constant
h 6.63 10?34 Joule second (J s)
Einstein suggested that some minimum energy (w)
is needed to pull an electron away from a metal.
If the quantum energy E lt w, no electron comes
out.
hf KE w
Photons have properties of particles localized
in a small region of space, have energy and
momentum, and interact with other particles (like
billiard balls).
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X-rays
The wave theory of light and the quantum theory
of light complement each other.
In 1895 Wilhelm Roentgen discovered inverse
photoelectric effect. He observed glowing of a
fluorescent screen under a bombardment by
electrons. The discovered radiation was very
penetrating and was called X-rays. X-rays are
produced whenever fast electrons are suddenly
stopped. They turned out to be electromagnetic
waves of extremely high frequency.
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Matter Waves
In 1924 Louis de Broglie suggested that moving
objects in some respects act like waves.
A particle of mass m and speed v behaves like a
wave with wavelength ?, so that
h
Planks constant ? ------ ? de Broglie
wavelength --------------------------
mv
momentum
Later it was shown that electrons exhibit both
diffraction and interference, and their
wavelengths are in agreement with the de Broglie
wavelength.
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Wave Function
In water waves, the height of the water surface
varies. In sound waves, it is the air
pressure. In electromagnetic waves, it is
electric and magnetic fields.
In matter waves, the wave function ? (psi)
varies. ? 2 at a given place and time for a given
particle determines the probability of finding
the particle there at that time.
? 2 is called the probability density of the
particle.
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Uncertainty Principle
If a moving particle is a wave, then there are
limits on the accuracy of the measurements of its
position and speed.
The particle may be located anywhere within the
wave packet at a given time. The maximum of ? 2
is in the middle of the packet. However, the
particle can be found anywhere that ? 2 ? 0.
The uncertainty principle It is impossible to
know both the exact position and the exact
momentum of a particle at the same time.
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Summary
The discovery of the photoelectric effect gave
rise to the quantum theory of light. Matter can
also behave as a wave, like electromagnetic waves
can behave as particles. The uncertainty
principle is one of the most significant physical
laws. It implies that we cannot now future for
sure because we cannot know the present for
sure. Importance of the subject