Download Quantum Theory of Light. Matter Waves.

Lecture 15
Quantum Theory of Light.
Matter Waves.
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Photoelectric effect
Photons
De Broglie Waves
Uncertainty Principle
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.
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.
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.
Photons
E=hf
E = quantum energy, f = frequency, h= Planck’s 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 < 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).
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.
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
Plank’s 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.
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.
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.
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