Transcript Lecture 11b - Atomic Physics & Nuclear Reactions

Lecture 11b
Atomic Physics & Nuclear Reactions
Copyright © 2009 Pearson Education, Inc.
Units of Chapter 37
•Early Models of the Atom
• Atomic Spectra: Key to the Structure of the
Atom
• The Bohr Model
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37-9 Early Models of the Atom
It was known that atoms were electrically neutral,
but that they could become charged, implying
that there were positive and negative charges
and that some of them could be removed.
One popular atomic model
was the “plum-pudding”
model:
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37-9 Early Models of the Atom
This model had the atom consisting of a bulk
positive charge, with negative electrons buried
throughout.
Rutherford did an experiment that showed that
the positively charged nucleus must be
extremely small compared to the rest of the
atom. He scattered alpha particles – helium
nuclei – from a metal foil and observed the
scattering angle. He found that some of the
angles were far larger than the plum-pudding
model would allow.
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37-9 Early Models of the Atom
The only way to account for the large angles
was to assume that all the positive charge was
contained within a tiny volume – now we know
that the radius
of the nucleus
is 1/10,000
that of the
atom.
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37-9 Early Models of the Atom
Therefore, Rutherford’s
model of the atom is
mostly empty space:
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37-10 Atomic Spectra: Key to the
Structure of the Atom
A very thin gas heated in a discharge tube emits
light only at characteristic frequencies.
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37-10 Atomic Spectra: Key to the
Structure of the Atom
An atomic spectrum is a line spectrum – only
certain frequencies appear. If white light passes
through such a gas, it absorbs at those same
frequencies.
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37-10 Atomic Spectra: Key to the
Structure of the Atom
The wavelengths of electrons emitted from
hydrogen have a regular pattern:
This is called the Balmer series. R is the
Rydberg constant:
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37-10 Atomic Spectra: Key to the
Structure of the Atom
Other series include the Lyman series:
and the Paschen series:
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37-10 Atomic Spectra: Key to the
Structure of the Atom
A portion of the complete spectrum of hydrogen
is shown here. The lines cannot be explained by
the Rutherford theory.
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37-11 The Bohr Model
Bohr proposed that the possible energy states
for atomic electrons were quantized – only
certain values were possible. Then the spectrum
could be explained as transitions from one level
to another.
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37-11 The Bohr Model
Bohr found that the angular momentum
was quantized:
.
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37-11 The Bohr Model
An electron is held in orbit by the Coulomb
force:
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37-11 The Bohr Model
Using the Coulomb force, we can calculate the
radii of the orbits:
.
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37-11 The Bohr Model
The lowest energy level
is called the ground
state; the others are
excited states.
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Energy Levels for Hydrogen Atom –
Bohr Model
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Ionization Energy
Ionization energy (or binding energy) is the
minimum energy required to remove an electron
from an atom initially at the ground state.
Example:
Ionization energy for hydrogen atom is 13.6 eV.
This is precisely the energy needed to remove an
electron from the lowest state E1 = 13.6 eV to
E = 0 where it can be free.
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37-11 The Bohr Model
Example 37-13: Wavelength of
a Lyman line.
Use this figure to determine
the wavelength of the first
Lyman line, the transition from
n = 2 to n = 1. In what region of
the electromagnetic spectrum
does this lie?
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37-11 The Bohr Model
Example 37-14: Wavelength of a Balmer
line.
Determine the wavelength of light
emitted when a hydrogen atom makes a
transition from the n = 6 to the n = 2
energy level according to the Bohr
model.
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37-11 The Bohr Model
Example 37-15: Absorption
wavelength.
Use this figure to determine
the maximum wavelength
that hydrogen in its ground
state can absorb. What would
be the next smaller
wavelength that would work?
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Summary of Chapter 37
•Rutherford showed that atom has tiny nucleus.
• Line spectra are explained by electrons having
only certain specific orbits.
• Ground state has the lowest energy; the others
are called excited states.
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X-ray Production by X-ray tube
(Giancoli Chp. 35 p.938)
Electrons emitted by
a heated filament in a
vacuum tube are
accelerated by a high
voltage. When they
strike the surface of
the anode, the
‘target’, X-rays are
emitted.
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X-ray Spectrum (Giancoli Chp. 39 p.1055)
Spectrum of X-ray
emitted from a
molybdenum target
in an X-ray tube
operated at 50 kV.
The spectrum
consists of the
continuous part
(with cutoff o) and
the discrete part
(characteristic
peaks)
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35-10 X-Rays and X-Ray Diffraction
The wavelengths of X-rays are very short.
Diffraction experiments are impossible to do with
conventional diffraction gratings.
Crystals have spacing between their layers that
is ideal for diffracting X-rays.
X-ray Diffraction (Giancoli p.939)
Bragg equation for constructive interference:
2d sin  = m
m = 1, 2, 3, …
d = the spacing between two adjacent
plane of the crystal
 = the angle between the X-ray & the plane of the
crystal (grazing angle)
 = wavelength of the X-ray
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Units of Chapter 42
• Nuclear Reactions and the Transmutation of
Elements
• Nuclear Fission
• Nuclear Fusion
42.1 Nuclear Reactions and the
Transmutation of Elements
A nuclear reaction is the process in which a
nucleus is struck by another nucleus or
particle transforming the original nucleus into
another nucleus.
If the original nucleus is transformed into
another, this is called transmutation.
An example:
42.1 Nuclear Reactions and the
Transmutation of Elements
Energy and momentum must be conserved in
nuclear reactions.
Generic reaction:
The reaction energy, or Q-value, is the sum
of the initial masses less the sum of the
final masses, multiplied by c2:
Nuclear Fission
A massive nucleus splits into fragments,
releasing energy in the process.
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42.3 Nuclear Fission
Example:
After absorbing a neutron, a
uranium-235 nucleus will split
into two roughly equal parts.
One way to visualize this is to
view the nucleus as a kind of
liquid drop.
42.3 Nuclear Fission
Conceptual Example 42-5: Counting
nucleons.
Identify the element X in the fission
reaction
42.4 Nuclear Fusion
Two small nuclei fuse together to form a
larger nucleus, releasing energy in the
process.
Example 42-7: Fusion energy release.
One of the simplest fusion reactions
2
involves the production of deuterium, 1H ,
from a neutron and a proton:
1
1
H + n  H + γ.
2
1
42.4 Nuclear Fusion
The Sun creates power by fusing hydrogen
into helium through the following set of
reactions: