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Unit 12: Part 2
Quantum Physics
Overview
Quantization: Planck’s Hypothesis
Quanta of Light: Photons and the
Photoelectric Effect
Quantum “Particles”: The Compton Effect
The Bohr Theory of the Hydrogen Atom
A Quantum Success: The Laser
Quantization: Planck’s Hypothesis
An ideal blackbody absorbs all
incoming radiation and re-emits it
in a spectrum that depends only
on temperature.
Quantization: Planck’s Hypothesis
The peak wavelength and total power increase
with temperature.
However, classical theory does not predict
this result; instead, it predicts a phenomenon
referred to as the “ultraviolet catastrophe.”
Quantization: Planck’s Hypothesis
Why a catastrophe? The
classical theory predicts
that the intensity of
radiation increases
without limit at shorter
and shorter
wavelengths. This
requires an infinite
amount of energy and is
obviously wrong.
Quantization: Planck’s Hypothesis
Planck realized that the ultraviolet catastrophe
goes away if we assume that the possible
values of the energy of electromagnetic
radiation are not continuous, but rather come in
little “packets,” whose energies are given by:
The constant h is called Planck’s constant:
Quantization: Planck’s Hypothesis
Planck was able to reproduce the
correct frequency spectrum using this
assumption, but he did not know quite
what to make of it.
Quanta of Light: Photons and the
Photoelectric Effect
Einstein proposed that not only must the
energy of thermal radiators in a hot substance
be quantized, the radiation they emit must be
quantized as well. He called these quanta
“photons.” Their energy depends on the
frequency of the light:
Quanta of Light: Photons and the
Photoelectric Effect
Some metallic materials
are photosensitive—
they emit electrons
when light shines on
them. The current
produced by these
electrons can be
measured, as can their
kinetic energy.
Quanta of Light: Photons and the
Photoelectric Effect
For a given material and
wavelength, increasing
the intensity of light
increases the current;
increasing the voltage
does not. The stopping
voltage, V0, indicates
the kinetic energy of the
emitted electrons:
Quanta of Light: Photons and the
Photoelectric Effect
The maximum kinetic energy increases
linearly with the frequency; below a cutoff
frequency, characteristic of each material, no
electrons will be emitted no matter how
intense the light.
The wave theory of light cannot explain this;
only the photon theory can.
Quanta of Light: Photons and the
Photoelectric Effect
Quanta of Light: Photons and the
Photoelectric Effect
The minimum amount of work required to free
an electron is called the work function:
Quanta of Light: Photons and the
Photoelectric Effect
Conservation of energy in the
photoelectric effect
Quanta of Light: Photons and the
Photoelectric Effect
The cutoff frequency, below which no
electrons will be emitted no matter how
intense the light, is given by:
Quanta of Light: Photons and the
Photoelectric Effect
One application of the photoelectric effect: the
“electric eye”
3 Quantum “Particles”: The
Compton Effect
Compton scattering occurs when an X-ray
scatters from a material. The scattered ray
has a longer wavelength that depends on the
scattering angle but not on the material.
Quantum “Particles”: The Compton
Effect
The photon acts as a particle,
transferring some of its energy to
the electron. Its own energy is
less, so the wavelength is longer.
is called the Compton
wavelength of the electron:
The Bohr Theory of the Hydrogen
Atom
Atoms are observed to emit and absorb
photons of particular wavelengths; each type
of atom has its own set of wavelengths.
An empirical formula was found that gives the
four visible spectral lines of hydrogen:
R, the Rydberg constant, has a value of
1.097 × 10–2 nm–1.
The Bohr Theory of the Hydrogen
Atom
In the Bohr model, the electron is in orbit
around the nucleus, with the centripetal force
being provided by the Coulomb force.
This gives possible
electron energies of
The Bohr Theory of the Hydrogen
Atom
In order to explain atomic spectra, Bohr then
made an assumption about quantization:
Bohr assumed that the angular momentum of the
electron was quantized and could have only discrete
values that were integral multiples of h/2π, where h
is Planck’s constant.
The Bohr Theory of the Hydrogen
Atom
We can use this to find the quantized radius
and energy:
The Bohr Theory of the Hydrogen
Atom
This leads to an allowed set of orbits and
energy levels.
The Bohr Theory of the Hydrogen
Atom
Photons are emitted or absorbed
when an electron makes a
transition between energy
levels. As the energy levels are
quantized, the photon
wavelengths can only take on
certain values.
The Bohr Theory of the Hydrogen
Atom
The energy required for a transition between
level ni and level nf is:
The Bohr Theory of the Hydrogen
Atom
This gives the observed series of spectral
lines.
A Quantum Success: The Laser
Some atoms have what are called metastable
states: they are excited states, but with
relatively long lifetimes. They are responsible
for phosphorescence—things that glow in the
dark.
If an electron is in a metastable state, it may
return to a lower state spontaneously; it may
also return to a lower state after absorbing a
photon of the correct energy. This is called
stimulated emission.
A Quantum Success: The Laser
It is possible to get a material in a condition
where there are more electrons in a
metastable state than in lower states—this is
called a population inversion. In this case,
there may be more stimulated emission than
absorption.
A Quantum Success: The Laser
In a helium–neon laser, the helium is first
“pumped” into an excited state by collisions
with electrons. Then the helium collides with
neon atoms, exciting them into the metastable
state. A spontaneous emission then excites
subsequent stimulated emissions.
A Quantum Success: The Laser
To make an actual laser, the helium and neon
are placed in a tube with a fully reflecting
mirror on one end and a partially reflecting
mirror on the other.
A Quantum Success: The Laser
Light from a laser is
coherent and
monochromatic; this
makes it very useful in
a number of
applications.
A Quantum Success: The Laser
Holograms use coherent laser light to produce
a three-dimensional image.
Review
Thermal radiation depends only on the
temperature of the radiating body. The peak
wavelength increases with temperature.
Classical theory could not predict the thermal
radiation spectrum; Planck did so by assuming
that the energies of the atoms in the material
were quantized.
Einstein explained the photoelectric effect by
assuming that light energy is also quantized:
Review
Light scattering off atomic electrons is called
the Compton effect. The scattered light has a
longer wavelength:
Bohr model of the hydrogen atom: electron
is in orbit around proton, centripetal force is
provided by Coulomb force. Only certain
energy levels are allowed.
Electrons making transitions between
energy levels emit radiation of particular
wavelengths.
Review
A metastable state is an energy state with a
relatively long lifetime.
Stimulated emission may occur from a
metastable state.
A laser uses stimulated emission to produce a
beam of monochromatic, coherent light.