Transcript Document 7801079

Chapter 40
Introduction to Quantum Physics
PHY 1371
Dr. Jie Zou
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Outline
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Blackbody radiation and Planck’s
Hypothesis
The photoelectron effect
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Blackbody
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Black body: A black body is
an ideal system that absorbs
all radiation incident on it.
Black body radiation: The
electromagnetic radiation
emitted by the black body is
called black-body radiation.
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Black-body radiation
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Two experimental findings:
1.
The total power of the emitted
radiation increases with temperature.
Stefan’s law: P = AeT4.
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2.
The intensity on the y-axis is
the intensity per wavelength.
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: Stefan-Boltzmann constant = 5.670 x
10-8 W/m2·K4; e: the emissivity of the
surface.
Stefan’s law for a black body: I = T4.
The peak of the wavelength
distribution shifts to shorter
wavelength as the temperature
increases. Wien’s displacement
law: maxT = 2.898 x 10-3 m·K.
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Early attempts of explanation
using classical ideas
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Rayleigh-Jeans law:
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I(, T) = 2ckBT/ 4.
At long wavelengths, the Rayleigh-Jeans
law is in reasonable agreement with
experimental data, but at short
wavelengths major disagreement is
apparent.
Ultraviolet catastrophe: the
energy emitted by any black body
will become infinite in the limit of
zero wavelength according to
classical theory – a mismatch of
theory and experiment.
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Planck’s theory of black-body
radiation
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Planck’s two assumptions concerning
the nature of the atomic oscillators:
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The energy of an oscillator can have only
certain discrete values En: En = nhf.
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German Physicist
Max Planck
The oscillators emit or absorb energy when
making a transition from one quantum state
to another. The entire energy difference in
the transition is emitted or absorbed as a
single quantum of radiation.
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n: a positive integer, a quantum number that
describes an allowed state of a system; f:
frequency of oscillation; h: Planck’s constant.
Energy is quantized. Quantum state.
Energy-level diagram
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An energy-level diagram
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Planck’s theoretical expression
for I(, T)
2hc 2
I  , T   5 hc / k BT
 e
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
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h: Planck’s constant (a
fundamental constant of nature).
h = 6.626 x 10-34 J·s
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The photoelectric effect
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Photoelectric effect:
Light incident on certain
metallic surfaces causes
electrons to be emitted
from those surfaces.
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Features of the photoelectric
effect
Dependence of photoelectron kinetic energy
on light intensity
1.
Experimental result: The maximum kinetic energy
of photoelectrons is independent of light intensity.
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Time interval between incidence of light and
ejection of photoelectrons
2.
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Experimental result: Electrons are emitted from
the surface of the metal almost instantaneously,
even at very low light intensities.
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Features of the photoelectric
effect (Cont.)
3. Dependence of ejection of electrons on light
frequency
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Experimental result: No electrons are emitted if
the incident light frequency falls below some
cutoff frequency fc, of which the value
depends on the material.
4. Dependence of photoelectron kinetic energy
on light frequency
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Experimental result: The maximum kinetic
energy of the photoelectrons increases with
increasing frequency.
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Einstein’s explanation of the
photoelectric effect
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Photons: Einstein assumed that light (or any
other electromagnetic wave) of frequency f
can be considered a stream of quanta,
regardless of the source of the radiation.
These quanta are called photons.
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Energy of each photon: E = hf.
Einstein’s model of photoelectric effect: A
photon of the incident light gives all its
energy hf to a single electron in the metal.
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The energy transfer is accomplished via a one
photon-one electron event.
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The maximum kinetic energy
of photoelectrons
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Kmax = hf - 
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: the work function of the metal.
The work function represents the
minimum energy with which an
electron is bound in the metal.
Einstein’s model predicts a linear
relationship between Kmax and the
light frequency f, which is confirmed
by experimental observation.
Cutoff frequency fc and cutoff
wavelength c: fc = /h and c =
hc/.
Stopping potential Kmax = e Vs.
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An application of photoelectric
effect – the photomultiplier tubes
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Homework
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Ch. 40, P. 1314, Problems: #2, 4, 14.
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