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Lecture
8: The Hydrogen Atom
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| Astronomy
101/103 |
Terry
Herter, Cornell University
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Lecture
Topics
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The
Spectrum of Hydrogen
Ionization
of atoms
Learn
how these emissions and absorptions are useful to astronomy.
- Each
element, ion, or molecule has a unique signature
- These
signatures are the Rosetta Stone of Astronomy
21-cm
Emission from Hydrogen
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The Spectrum
of
Hydrogen
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Hydrogen
has one electron, so it is the simplest of the elements
in terms of its spectrum.
Like
other elements Hydrogen has discrete emission or absorption
lines which result when the electron move between energy
levels.
- Note,
to move "up" a level, a photon of exactly the
correct energy (or wavelength) is required.
The
Hydrogen atom can emit and absorb light at discrete wavelengths
in the ultraviolet, visible, infrared, and radio.
In
the visible the lines are called the Balmer lines.
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Hydrogen
Balmer
Spectrum
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A
schematic representation of the hydrogen Balmer spectrum
is show below.
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Aside
(In case you are interested)
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The
Balmer series derives its name from Johann
Jacob Balmer who (in 1885) found a series
that fits wavelengths of the set of four
emission lines (Ha,
Hb, Hg,
Hd)
from hydrogen discovered by Anders Ångström.
Ångström found the first
three lines in 1862 and by 1871 had discovered
a fourth line
and measured the wavelengths to high accuracy.
Balmer
was not a spectroscopist or even an experimentalist.
He was a high school
teacher
for girls in mathematics and interested
in numerology. A friend suggested he
work on
the problem!
In
1890 Johannes Robert Rydberg generalized
Balmer's formula to cover other hydrogen
spectral lines (and also introduced the
concept
of the wave number, which is the reciprical
of the wavelength). Rydberg also applied
the concept to akali metals and other elements.
Of course, none of this explained where the
series came from. This was left to Niels
Bohr and quantum mechanics. |
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Hydrogen
Energy
Levels
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energy level diagram for hydrogen is given below. The various
hydrogen spectral "series" are defined by their
ending (bottom) level, e.g. for the Lyman series all electronic
transitions go to level one, while for the Balmer series all
electrons go to level two.
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Aside
(In case you are interested)
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are names for series where the electron goes to
levels 3, 4, 5, or 6 that are respectively
called
the Paschen, Brackett, Pfund and Humphreys
series. |
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Energy
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The
energies in atoms are usually expressed in electron volts
(eV).
For
instance, the energy difference between n=2 and n=1 in H
is 10.2 eV.
Since
E = hc/l, l
= 1216 A
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Aside
(In case you are interested)
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| The
electron volt is defined as the work required
to move an electron through a potential difference
of 1 volt. In "electrostatics" the force
on a charged particle is given by F = q E, where
q = charge and E is the electric field strength.
For a uniform electric field, V = E d where V
is the electric potential (measured in volts)
and d is the distance moved (note that the electric
field has units of volts/meter). Then we have
Energy = F d = q V. |
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Hydrogen
Spectral
Lines
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The
spectral lines in the ultraviolet are call the Lyman series.
In the visible these are called the Balmer series.
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Series
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Designation
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Transition
(Levels)
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Wavelength
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Lyman
(UV)
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Lya
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2-1
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1215.7
A
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Lyb
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3-1
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1025.7
A
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Lyg
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4-1
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972.53
A
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...
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limit
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infinity-1
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911.5
A
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Balmer
(visible)
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Ha
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3-2
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6562.8
A
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Hb
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4-2
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4861.3
A
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Hg
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5-2
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4340.5
A
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...
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limit
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infinity-2
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3646.0
A
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"Transition"
indicates the change in energy level (designated by the
principle quantum number) of the electron. For instance,
3 - 1 implies the electron falls from n = 3 to n = 1 in
the atom.
The
term "limit" indicates the limit to reach the
continuum (see below). If a photon has more energy than
this threshold (shorter wavelength) it can ionize hydrogen.
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Spectral
Line
Notes
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Key
Features of the Atoms
The
energy levels get closer together as the quantum numbers
get larger.
The
greater the difference between the quantum numbers, the
larger the energy of the photon emitted or absorbed.
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The
Continuum
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If
an electron is given enough energy (via a photon or by
other means) it can escape the atom. The electron is then
"unbound" and the quantization of energy levels
disappears.
The
continuum is shown schematically in the energy level diagram
below, above the n = infinity principle quantum number.
Photons with energy exceeding 13.6 eV can promote the
electron into the continuum -- freeing the electron from
the hydrogen atom.
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Ionization
and
Ions
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If
a photon has enough energy, it can ionize an atom,
i.e. promote an electron into the continuum.
An
atom becomes an ion when one or more electrons have
been removed.
Though
adding an extra electron also creates an ion, it is much
more difficult and rare.
Many
atoms in space are ionized. Fortunately each ion
has its
own spectral signature.
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Hydrogen
Ionization
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The
ionization energy of hydrogen is 13.6 eV.
Ionizing
an electron from the ground state (n = 1) of hydrogen requires
photons of energy 13.6 eV or greater.
=>
l < 912 A
Ionized
hydrogen is just a proton by itself!
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Helium
Ions
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All
elements can be ionized by removing one or more electrons.
The example of helium is shown below.
It
takes progressively more energy to remove successive electrons
from an atom.
- That
is, it is much harder to ionize He II than He I.
Note:
You can not have He IV!
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Notation
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Astronomers
use the following notation to indicate the ionic state of
an atom.
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Suffix
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Meaning
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Examples
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I
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neutral
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He I, O I
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II
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once ionized
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He II, O II
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III
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twice ionized
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He III, O III
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IV
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three times ionized
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O IV, Ne IV
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Spectral
Signatures
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Spectral
Signatures: Astronomy's Rosetta Stone
The
set of spectral lines associated with a given ion
are unique and are of fundamental importance to astronomy.
We
call this the "spectral signature" of an ion.
Allows
the identification of elements across the galaxy and universe.
- With
spectral signatures we can identify oxygen, carbon, iron,
etc.
In
addition these signatures provide information on:
- Chemical
composition of the stars
- Abundances
of the elements
- Physical
conditions of the gases such as densities
and temperatures
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Emission
from
Solids
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Solid
materials have a continuous spectrum rather than a discrete
one.
This
is different from individual atoms.
Examples:
- Tungsten
filament light bulb - continuous
- Fluorescent
lamp - discrete
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Hydrogen
21-cm
Radiation
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An
important spectral line in astronomy for measuring
the gas between stars is the 21-cm line of Hydrogen.
- This
is in the radio part of the spectrum.
The
n = 1 level (ground state) of H is actually "split" into
2 levels separated by a very small energy.
- This
splitting is due to the fact that the electron and
proton have intrinsic spin, i.e. they behave like
small magnets.
- When
the North poles are aligned the energy is higher
than when they are not.
The
figure below illustrates the "spin flip" that
cause the emission of a 21-cm photon.
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A
21-cm photon is emitted when poles go
from being aligned to opposite (a spin
flip).
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This
emission from a small number of H-atoms is very weak,
but hydrogen is very plentiful in space.
- So
we see a lot of 21-cm radiation from our galaxy.
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