By the end of the 19th century, the scientific community
generally agrees on the nature of light:
Light is a WAVE.
 Light energy travels from a source as a continuous
electromagnetic wave.
 The amount of light energy in emitted from the source is
related to its intensity.
The brighter the light, the more energy emitted by the
source.
 The frequency of the light wave determines its type -- visible,
infrared, gamma, etc. THE FREQUENCY OF THE LIGHT
WAVE HAS NOTHING TO DO WITH ITS ENERGY
CONTENT.
Blackbody radiation
Objects give off light (glow) when they are heated.
Wave theory explains:
Vibrating (‘hot’) atoms radiate energy away by producing
light waves
Wave theory can NOT explain:
Why red light corresponds to lowest temperature glowing
objects. (Why is there a connection between temperature
and observed color?)
Max Planck creates idea that object is giving off the heat energy
in chunks (quanta)
photoelectric effect
The emission of electrons from a metal when light hits it.
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Wave theory of light explains:
Electron absorbs energy of light wave, gaining enough KE
to escape pull of nucleus of metal atom.
Wave theory can NOT explain:
Why electrons are only emitted if the incident light is at or
above a certain minimum frequency – called the cutoff
frequency.
If the energy of light is related to its intensity, then only
the brightness of the light source should matter; the
emission of electrons should happen with any
frequency of light used, as long as it was bright
enough.
Albert Einstein (1905) explained the cutoff frequency using
Planck’s idea of a quantum (discrete bundle) of light energy
 Photon Theory of Light
 Light energy is emitted by the source as a stream of
photons – light energy quanta
 The energy content of a photon is related to the source
frequency
E = hƒ
(h = 6.63 x 10-34 J∙s)
Planck’s
Constant
Ex: A photon of orange light (ƒ = 5.0 x 1014 Hz) has an energy
content of:
3.3 x 10-19 J
 When a photon hits an electron it is completely
absorbed. If the source frequency is high enough ( fc)
the energy in the photon is sufficient to allow the
electron to escape the nucleus. If ƒsource < ƒc the energy
of the photon will not be sufficient to free the electron.
Question:
The cutoff frequency of a certain metal is 3.75 x
1014 Hz. How many 1.75 x 10-19 J photons will it
take to dislodge a single electron from this
metal?
 Another application of the photon theory of light – Compton
Effect
 X-rays scattered by a crystal have a lower frequency
than they did going into the crystal. The amount of
change in ƒ depends upon the “scattering angle”
ƒ < ƒO
ƒ <<< ƒO
X-ray
source
ƒO
C
R
Y
S
T
A
L
ƒ = ƒO
ƒ << ƒO
The larger the
“scattering angle”, the
lower the frequency
 Photons coming from source “collide” with crystal
particles, transferring some energy to them.
Larger scattering angle  more energy lost by
photon  lower frequency
http://www.student.nada.kth.se/~f93-jhu/phys_sim/compton/Compton.htm
 Louis DeBroglie: hypothesizes that if light has particle
characteristics, perhaps particles have wave characteristics.
 He combined the photon equation (E = hƒ) with the energymass equivalence equation (E = mc²):
mc² = hƒ
(‘c’ denotes light speed, for particles...)
mv² = hƒ
mv² = h(v/λ)
mv = h/λ
h

p
Ex: A baseball of mass 145 grams moving at 40.0 m/s would
have a “wavelength” of...
1.14 x 10-34 m
(Macroscopic objects have wavelengths much too
small to be observable)
How about an electron moving at 300 m/s:
what is its wavelength?
DeBroglie’s hypothesis was tested with the ELECTRON DOUBLE-SLIT
EXPERIMENT.
Laser
wave result
Particle
Beam
Particle result
Electron
Beam
Schrodinger’s idea
Quantum Dice activity
?
?
?
?
?
Max Born (German physicist) says  this ‘matter’ wave
represents a probability function that governs the motion of the
particle.
It identifies where the particle is most likely to be found.
A particle moving with a specific momentum has an associated
PSI WAVE (Ψ) of specific wavelength.
|
λ
|
A
Δx
λ  momentum of particle
( from mv = h/λ)
Δx  possible location of particle
A  probability of particle being in that location
(A² = probability density)
* No certainty to location of particles, just probabilities –
like rolling dice.
Since waves have a tendency to spread out, Δx would be
infinite in extent – the particle would have an equal
probability of being ANYWHERE!
To ‘localize’ the particle, decrease the Δx of its psi wave by
adding other Ψ’s of different wavelengths. This produces a
wave packet:
Δx
(much smaller)
* PLUS: The amplitude of the wave is largest in the middle
– the particle is most likely to be at the center of
the Δx region.
The trade-off: Now the particle’s psi wave is made of several
different wavelengths, which means the particle has a range of
possible momenta, not a specific momentum value (like it had
originally).
IN BECOMING MORE CERTAIN OF THE PARTICLE’S
LOCATION, YOU BECAME LESS CERTAIN OF ITS
MOMENTUM!
http://www.fen.bilkent.edu.tr/~yalabik/applets/collapse.html
Heisenberg Uncertainty Principle
It is impossible to know the exact location and momentum of a
particle simultaneously. The more certain you are of one
quantity, the less certain the other one becomes.
Δp ∙ Δx  h / 2π
* Momentum and location are mutually exclusive quantities.
(This goes completely against the deterministic view of
the universe.)
CONSEQUENCES OF THIS THEORY:
•
The subatomic world is made of particles whose motions are
governed by probability functions. (Light is made of
particles; its wave properties are due to the probability
waves associated with its motion.)
THESE PARTICLES ARE ALWAYS IN MOTION.
•
•
Individual particle events – where one particle ends up after
traveling through an environment – are completely random.
(The results of a collection of these events can be predicted
statistically.)
This uncertainty (randomness) is part of nature; it is not due
to our lack of intelligence or technology.
http://www.fen.bilkent.edu.tr/~yalabik/applets/collapse.html
Quantum Tunneling
Place a charged particle in a “cage” made by insulating
material.
Classical physics says the particle can’t escape.
If “cage” dimensions are small enough, the particle’s psi
wave could exist outside of the cage.
Therefore, the particle would have a non-zero
probability of existing outside of the box.
-
e
At some point, the particle may disappear from inside
the cage and reappear outside of it – effectively
tunneling through the barrier!
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Anti-Matter
Predicted to exist by Paul Dirac. (1930’s)
Another form of Heisenberg Uncertainty Principle says
ΔE ∙ Δt  h / 2π
This says that if the time interval is extremely small, the
energy of a region will be very uncertain.
Therefore, a region of empty space (which would
have zero energy over a large time interval) could
instantly contain a non-zero amount of energy.
This energy would exist in the form of two particles. One
would be an ordinary particle, the other with the same
mass but opposite charge (the anti-particle).
The anti-electron (positron) would have
the same mass as an electron but would
have a +1 charge.
This process, in which an energy fluctuation creates a
particle and its corresponding anti-particle, is known as
pair production.
If a particle and its corresponding anti-particle meet, they
will annihilate each other, producing pure energy. This
process is called pair annihilation.
Quantum Entanglement
If two particles are created together during some
interaction, their psi waves could be “connected”.
Changing the properties of one particle would cause a
similar change in the other particle, even though they
may be separated physically by a great distance!
Beam Splitter
(creates two
entangled
photons)
When this photon
reaches its far-away
lab destination, its
polarization is found
to be shifted 45°, just
like the other one!
Rotates
photon
polarization
45°
Photon
detected in
far-away
lab