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Summary
Lecture 33
Photoelectric effect: metals illuminated with light would release their electrons;
electromagnetic waves give their energy to the electrons, and this allows them
to escape from the surface of the metal.
KE max = eV0
Stopping voltage is reverse voltage needed to
stop all electrons from reaching the collector:
Wave-Particle Duality
Wave Nature of Matter
Early Model of Atom
Atomic Spectra
Photon theory can explain photoelectric effect while wave theory not.
(1) If the light intensity is increased, the number of electrons emitted increases,
but their KEmax is unchanged. (2) Below a “cutoff” frequency, f0, no electrons
are emitted, regardless of the intensity. (3) KEmax increases linearly with
frequency.
hf = KE max + W0
KE max = hf − W0
Compton found that the wavelength of scattered
photon was longer than the incident ones, and that
the wavelength depended on the scattering angle, φ.
λ'= λ +
h
(1 − cos φ )
m0 c
Photons passing through matter can result in four types of interactions:
(1) photoelectric effect, (2) atomic excitation, (3) Compton effect, and (4) pair
production, i.e. electron and positron.
Physics 112, Spring 2010, Apr 9, Lecture 33
Physics 112, Spring 2010, Apr 9, Lecture 33
Plank Constant
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Wave-Particle Duality
Planck's constant is
1) sets an upper limit to the amount of energy that can be absorbed or emitted
2) sets a lower limit to the amount of energy that can be absorbed or emitted
∗
∗
Diffraction and interference suggest light is a wave.
The photoelectric effect and the Compton effect point to light being a
particle (photon).
Which is right?
3) relates mass to energy
4) none of the given answers
This question has no answer; we must accept
Color and Energy
Which color in the visible spectrum is associated with the lowest
temperature?
1) blue
E = hf = h
2) green
Principle of complementarity: to understand an experiment, sometimes
we find an explanation using wave theory and sometimes using particle
theory.
c
λ
Waves and particles are just our interpretations of how light behaves.
3) orange
4) red
Physics 112, Spring 2010, Apr 9, Lecture 33
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Physics 112, Spring 2010, Apr 9, Lecture 33
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Wave Nature of Matter: De Broglie Hypothesis
Wavelength of Electron
In 1911 Louis de Broglie made a hypothesis (in his Ph.D. thesis):
Determine the wavelength of an electron that has been accelerated through a
potential difference of 100 V.
Electron and other moving particles possess wavelike properties.
λDe Broglie =
De Broglie wavelength:
1. The kinetic energy of an electron vs. acceleration:
h
mv
mv 2
= eV
2
h is the Plank constant .
2. The velocity of an electron:
v is the speed of the particle.
m is the mass of the particle.
v=
Louis de Broglie
The wave associated with any moving
particles has a specific wavelength.
2eV
(2)(1.6 ×10 −19 C )(100 V )
=
= 5.9 ×106 m / s
m
9.1×10 −31 kg
3. The wavelength of an electron:
What is an electron?
λ=
An electron is the set of its properties that we can measure.
m = 9.1 × 10 −31 kg
e = −1.6 × 10 −19 C
Physics 112, Spring 2010, Apr 9, Lecture 33
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Transmission Electron Microscope (TEM)
h
6.63 ×10 −34 J ⋅ s
=
= 1.2 ×10 −10 m = 0.12 nm
mv (9.1×10 −31 kg )(5.9 ×106 m / s )
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Physics 112, Spring 2010, Mar 1, Lecture 20
Scanning Electron Microscope (SEM)
Produces 2D images, best resolution ~0.1 – 0.5 nm
(~1000 times better than optical microscope).
Electrons are focused by magnetic coils.
Produces 3D images resolution typically ~5-10 nm.
Electron beam is scanned back and forth across the
object.
Question: why this is possible?
Eye of a fly.
Colorized TEM image of influenza virus particles.
Physics 112, Spring 2010, Apr 9, Lecture 33
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Physics 112, Spring 2010, Apr 9, Lecture 33
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Scanning Tunneling Microscope (STM)
Early Model of Atom
An even higher resolution can be achieved by using the wave properties
of the electrons.
It was known that atoms were electrically neutral,
but that they could become charged.
If you put a very small probe close to a surface, the wave properties of electrons
allow them to “jump” to the probe.
This implied the atom contained (+) and (-) charges
and some of them could be removed.
The up and down motion of the probe keeps the tunneling current constant.
In 1911, Rutherford made an experiment that showed
that the atom must contain an extremely small,
positively charged nucleus.
Ernest Rutherford
1871-1937
An image of 48 Fe atoms created
with an STM microscope.
He fired α particles – helium nuclei – at a
metal foil and observed the scattering angles.
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Physics 112, Spring 2010, Apr 9, Lecture 33
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Physics 112, Spring 2010, Apr 9, Lecture 33
Rutherford’s Model of Atom
Problem 3: Atomic Spectra
The last aspect that confused physicists was the light emission of a plasma of a
single type of atoms (atomic spectra).
Some α particles were scattered at very
large angles.
Every atom emits light at a characteristic set of frequencies; these frequencies
appear as “lines” if we send the light through a prism.
The only way to explain these large angles
was to assume that all the (+) charge and
most of the mass, was contained within a
tiny volume (nucleus).
First discovered and used by Bunsen and Kirchoff as a means to identify different
chemical elements (1859).
Hydrogen
Rutherford’s model
of the atom is mostly
empty space.
Helium
gold
Mercury
We now know
that the nucleus
is 1/10,000 of the
atom size.
Physics 112, Spring 2010, Apr 9, Lecture 33
Uranium
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Robert Bunsen
1811-1899
Physics 112, Spring 2010, Apr 9, Lecture 33
Gustav Kirchoff
1824-1887
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Once More: Dispersion of White Light by a Prism
Microwaves
White light
(mixture)
Emission Spectra
A sample of some gas in a glass tube emits light:
Radio
Light from
hot gas
Simple colors
Simple colors
Red
Orange
Yellow
Green
Blue
Violet
Prism
Prism
An emission spectrum consisting
of a few discrete colored lines.
Speed of red light has the ~1.97×108 m/s while speed of blue is ~1.95×108 m/s
Wavelength (nm)
If no absorption of light will occur, we can see a continuous spectrum:
Photon energy (eV)
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Physics 112, Spring 2010, Apr 9, Lecture 33
Emission spectra
Colored lines indicate that an object
emits electromagnetic waves only at
some certain wavelength (energy).
c
λ
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Photon
Absorption Spectra
What is a photon?
A sample of some gas in a glass tube absorbs light:
Gas in a tube
E = hf = h
1) an electron in an excited state
Simple colors
2) a small packet of electromagnetic energy that has particle-like properties
3) one form of a nucleon, one of the particles that makes up the nucleus
4) an electron that has been made electrically neutral
Prism
Electron Microscope
Dark
lines
An absorption spectra consisting
of a few discrete dark lines.
What advantage might an electron microscope have over a light
microscope?
Wavelength (nm)
Absorption spectra
Dark lines indicate an absorption at
certain wavelength (energy).
1) electrons are more powerful
E = hf = h
c
λ
Photon energy (eV)
2) shorter wavelengths are possible
3) longer wavelengths are possible
4) none of the given answers
Physics 112, Spring 2010, Apr 9, Lecture 33
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Physics 112, Spring 2010, Apr 9, Lecture 33
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