Quantum Mechanics and

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Quantum Mechanics and Atomic Spectroscopy
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Rutherford Atom (1911)
classically, any value of v or r is allowed.
e
r
Ze
Protons in nucleus. Electrons orbit like planets.
The neutron was not discovered until 1932
(Chadwick)
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Rutherford Atom (1911)
e
r
Ze
BUT,
As the electron moves in its orbit it is
accelerated, and therefore emits radiation.
Because energy is being radiated, the total
energy of the system must decrease become more
negative. This means v2 must increase and r must
get smaller. But smaller r and larger v also
imply greater acceleration and radiation. In
approximately 10-6 s the electron spirals into
the nucleus. Goodbye universe
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The solution lies in the wave-like property of
the electron and of all matter
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m
m
As you squeeze on the box, the particle in the
box has to move faster.
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8e-
270e-
2,000e-
60,000e-
Hitachi labs (1989)
At no time was more tha one electron present in
the beam in transit.
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Ground state of the hydrogen atom Neils Bohr
(1913)
(lowest possible energy state)
Must fit the wavelength of the electron inside a
circle of radius r, the average distance between
the electron and the proton.
r
e- p
new
as before
Note that PE goes as 1/r and KE goes as 1/r2
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For a single electron bound to a single
proton, i.e., hydrogen.
Energy
r
ro
At ro
Virial Theorem
Energy would have to be provided to the electron
to make it move any closer to the proton (because
itwould have to move faster), more energy than
e2/r can give.
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Bohrs First Postulate
For atoms with a single electron H, He, etc.
The only possible states of the electron
are those for which
n3
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In the full quantum mechanical solution the
electron is described by a wave function that
gives its probability for being found at any
particular distance from the nucleus. In the
simplest case these distributions are
spherical. The radius in the Bohr model is the
average radius but the energy is precise.
n 1 n2 n3
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Bohrs Second Postulate
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E.g.,
Lines that start or end on n1 are called the
Lyman series
Lines that start or end on n2 are called the
Balmer series
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Adjusting the energy of each state in hydrogen by
adding 13.6 eV (so that the ground state becomes
zero), one gets a diagram where the energies of
the transitions can be read off easily.
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Absorption Line Spectrum
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How are excited states populated?

• Absorb a photon of the right energy
• Collisions
• Ionization - recombination

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Fluorescent Light Fixture
red
green
violet
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He II strong, He I increasing from O4 to O9 H
prominent
He I lines dominate H increasing in strength
http//nedwww.ipac.caltech.edu/level5/Gray/Gray_co
ntents.html
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H lines reach maximum strength. Ca II growing. Fe
II, Si II, Mg II reach
H lines start to decrease in strength. Ca II
strong. Fe I growing in strength. Mg II
decreasing.
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Ca II lines strongest, H lines weak, neutral
metal lines strong. G-band of CH is strong.
H lines weak. Lines of neutral metals present but
weakening. Major characteristic is bands from
molecules like TiO and MgH
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Luminosity Classes
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Class I
Class V
These stars all have essentially the same
temperature and are spectral type M2. However,
based upon the strength of the Ca I 4227 A line,
one can distinguish red supergiants (Class I)
from ordinary red giants (Class III), and main
sequence stars (Class V).
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At other temperatures other lines are used to
distinguish luminosity class. Here, for F0, the
chief diagnostics are blends of Fe II and Ti II
lines at 4172-4178 A and similar blends at
4395-4400, 4417, and 4444 A.