Download Modern Physics 3-Atomic Physics

3/10/2015
Modern Physics 3
Atomic Physics-ch27
Physics 116
Eyres
Dalton model: Atom as billiard ball
• In 1803, John Dalton proposed a billiard ball model that viewed the
atom as a small solid sphere.
• According to Dalton, a sample of a pure element was composed of a
large number of atoms of a single kind.
• Each atom, regardless of type, contains an equal amount of positively
and negatively charged subcomponents so that each atom is
electrically neutral.
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Thomson model: Atom as plum pudding
• In 1897, J. J. Thomson hypothesized that electrons were the
negatively charged components of atoms.
• In his model, an atom was similar to a spherically shaped plum
pudding.
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Rutherford model: Atom as planetary system
• In 1909, Ernest Rutherford and his postdoctoral colleague Hans
Geiger hypothesized that the atom's mass was not spread uniformly
throughout the atom, but instead concentrated in a small region.
• Rutherford developed a new model of the atom in which a tiny
nucleus contained nearly all of the mass of the atom and all of its
positive charge.
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A difficulty
with the planetary model
• An accelerating electron emits electromagnetic radiation, and
this radiation has energy.
• Because the electron orbiting the nucleus is continually
accelerating, the electron-nucleus system should
continuously lose energy.
• The Rutherford model could not explain the stability of atoms.
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Spectra of low-density
gases and the need
for a new model
• Observations show that
different gases produce
different sets of spectral
lines.
• Scientists could not explain
where the lines came from.
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Spectra of low-density gases and the need
for a new model
• In 1885, Johann Balmer found a pattern in the wavelengths of the
visible spectral lines produced by hydrogen and represented it with
the following equation:
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Bohr's model of the atom: Quantized orbits
• In 1913, Danish physicist Niels Bohr developed a new model that explained
the line spectra and the stability of the atom.
• The structure of Rutherford's model, but imposed a restriction on the electron
orbits.
• The atom is made up of a small nucleus and an orbiting electron.
• The electron can occupy only certain orbits, n.
• When in these orbits, the electron does not radiate electromagnetic waves.
• When an electron transitions from one stable orbit to another, the atom's
energy changes.
• When the energy of the atom decreases, the atom emits a photon.
• To increase, the atom must absorb some energy, often a photon.
• Because the stable orbits are discrete, the atom can radiate or absorb only certain
specific amounts of energy.
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Energy states of the
Bohr model
• The energy of the atom is
inversely proportional to the
square of the quantum
number n:
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Emission and absorption of photons
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How lasers work
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Lasers
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Summary of quantum numbers
• Principal quantum number:
• Orbital angular momentum quantum number:
• Magnetic quantum number:
• Spin magnetic quantum number:
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Emission Spectra
Slide 29-30
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De Broglie waves and Bohr's third postulate
• For an electron wave to be
stable, an exact integer
number n of electron
wavelengths must be
wrapped around the
nucleus:
• This is precisely Bohr's third
postulate!
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Matter Waves
An electron beam passing
through a double slit produces
an interference pattern similar to
that for light.
=
=
1−
1−
=
=
=
=
Slide 28-18
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The Particle in a Box
2 =
2
=
=
=
=
2
2
The possible modes are reminiscent of those for
the modes of a stretched string. The possible
modes have different energies:
Slide 28-19
Colors of Dyes
The color of dyes results from the preferential absorption of certain
wavelengths of light. For certain dyes, such as the cyanine dye of
which a portion is illustrated below, we can determine the absorption
wavelengths by using a simple particle in a box model. The dye
molecules consist of symmetric pairs of rings joined at the center by
a chain of carbon atoms. Electrons of the bonds along the chain of
carbon atoms are shared among the atoms in the chain, but are
repelled by the nitrogen-containing rings at the end of the chain.
These electrons are thus free to move along the chain but not
beyond its ends. They look very much like a particle in a onedimensional box. For the molecule below, the effective length of the
“box” is 0.85 nm. What are the energies of the first five states?.
Slide 28-20
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Energy Levels and Quantum Jumps
For the dye molecule on the previous
slide, what are the energy values for
levels n=1, 2, 3, etc?
What wavelength light corresponds to a
transition between the energy levels n=4
and n=5?
What is the maximum photon energy
that could be emitted by the quantum
system with the energy level diagram
shown below? The minimum photon
energy?
A. 7.0 eV
B. 6.0 eV
C. 5.0 eV
D. 4.0 eV
E. 3.0 eV
F. 2.0 eV
G. 1.0 eV
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The uncertainty principle
• A connection exists
between the narrowness
of the slit and the
apparent y-component
of the electron's
momentum once it
passes through:
=
=
=
=
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Uncertainty principle for
energy
• Because a fundamental limit
exists on the determinability of
the momentum of a particle, a
fundamental limit should also
exist on the determinability of
the energy of the photon:
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